Articles

Existence and asymptotic properties of singular solutions of nonlinear elliptic equations in \(R^{n}\backslash\{0\}\)

Authors: Imed Bachar and Entesar Aljarallah

Solutions for a category of singular nonlinear fractional differential equations subject to integral boundary conditions

We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at ...

Authors: Debao Yan

Infinitely many solutions for the discrete Schrödinger equations with a nonlocal term

Authors: Qilin Xie and Huafeng Xiao

Solvability of a moving contact-line problem with interface formation for an incompressible viscous fluid

We investigate the free-boundary problem of a steadily advancing meniscus in a circular capillary tube. The problem is described using the “interface formation model,” which was originally introduced with the ...

Authors: Yoshiaki Kusaka

The sub-supersolution method for a nonhomogeneous elliptic equation involving Lebesgue generalized spaces

Authors: Giovany M. Figueiredo and A. Razani

On a nonlocal implicit problem under Atangana–Baleanu–Caputo fractional derivative

In this paper, we study a class of initial value problems for a nonlinear implicit fractional differential equation with nonlocal conditions involving the Atangana–Baleanu–Caputo fractional derivative. The app...

Authors: Abeer S. Alnahdi, Mdi Begum Jeelani, Mohammed S. Abdo, Saeed M. Ali and S. Saleh

Some notes on conformable fractional Sturm–Liouville problems

Authors: Wei-Chuan Wang

Existence of groundstates for Choquard type equations with Hardy–Littlewood–Sobolev critical exponent

Authors: Xiaowei Li and Feizhi Wang

Existence of ground state solutions for a class of Choquard equations with local nonlinear perturbation and variable potential

Authors: Jing Zhang and Qiongfen Zhang

Fractional N-Laplacian boundary value problems with jumping nonlinearities in the fractional Orlicz–Sobolev spaces

We investigate the multiplicity of solutions for problems involving the fractional N-Laplacian. We obtain three theorems depending on the source terms in which the nonlinearities cross some eigenvalues. We obt...

Authors: Q-Heung Choi and Tacksun Jung

Enhanced algorithms for solving the spectral discretization of the vorticity–velocity–pressure formulation of the Navier–Stokes problem

The objective of the article is to improve the algorithms for the resolution of the spectral discretization of the vorticity–velocity–pressure formulation of the Navier–Stokes problem in two and three domains....

Authors: Mohamed Abdelwahed, Nejmeddine Chorfi and Henda Ouertani

High perturbations of a new Kirchhoff problem involving the p-Laplace operator

In the present work we are concerned with the existence and multiplicity of solutions for the following new Kirchhoff problem involving the p-Laplace operator:

Authors: Zhongyi Zhang and Yueqiang Song

The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems

In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville d...

Authors: Zihan Li, Xiao-Bao Shu and Tengyuan Miao

On positive solutions of second-order delayed differential system with indefinite weight

In this paper, we study the existence of positive solutions of a second-order delayed differential system, in which the weight functions may change sign. To prove our main results, we apply Krasnosel’skii’s fi...

Authors: Fanglei Wang and Ran Ding

On a power-type coupled system with mean curvature operator in Minkowski space

Authors: Zhiqian He, Yanzhong Zhao and Liangying Miao

On Glassey’s conjecture for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Consider nonlinear wave equations in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions ...

Authors: Kimitoshi Tsutaya and Yuta Wakasugi

Ground state solutions and infinitely many solutions for a nonlinear Choquard equation

Authors: Tianfang Wang and Wen Zhang

On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum

In this paper, by using the energy estimates, the structure of the equations, and the properties of one dimension, we establish the global existence and uniqueness of strong and classical solutions to the init...

Authors: Menglong Su

Classification of nonnegative solutions to static Schrödinger–Hartree–Maxwell system involving the fractional Laplacian

Authors: Yunting Li, Yaqiong Liu and Yunhui Yi

On strong singular fractional version of the Sturm–Liouville equation

The Sturm–Liouville equation is among the significant differential equations having many applications, and a lot of researchers have studied it. Up to now, different versions of this equation have been reviewe...

Authors: Mehdi Shabibi, Akbar Zada, Hashem Parvaneh Masiha and Shahram Rezapour

On the asymptotic behavior of solutions of anisotropic viscoelastic body

The quasistatic problem of a viscoelastic body in a three-dimensional thin domain with Tresca’s friction law is considered. The viscoelasticity coefficients and data for this system are assumed to vary with re...

Authors: Yassine Letoufa, Hamid Benseridi, Salah Boulaaras and Mourad Dilmi

Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that ...

Authors: Nyurgun Lazarev

Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate

We introduce a diffusive SEIR model with nonlocal delayed transmission between the infected subpopulation and the susceptible subpopulation with a general nonlinear incidence. We show that our results on exist...

Authors: Xin Wu and Zhaohai Ma

Singularly perturbed quasilinear Choquard equations with nonlinearity satisfying Berestycki–Lions assumptions

Authors: Heng Yang

Elliptic problem driven by different types of nonlinearities

Authors: Debajyoti Choudhuri and Dušan D. Repovš

The principal eigenvalue of some nth order linear boundary value problems

The purpose of this paper is to present a procedure for the estimation of the smallest eigenvalues and their associated eigenfunctions of nth order linear boundary value problems with homogeneous boundary conditi...

Authors: Pedro Almenar and Lucas Jódar

The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems

In this paper, we are concerned with the eigenvalue gap and eigenvalue ratio of the Dirichlet conformable fractional Sturm–Liouville problems. We show that this kind of differential equation satisfies the Stur...

Authors: Yan-Hsiou Cheng

New interpolation spaces and strict Hölder regularity for fractional abstract Cauchy problem

We know that interpolation spaces in terms of analytic semigroup have a significant role into the study of strict Hölder regularity of solutions of classical abstract Cauchy problem (ACP). In this paper, we fi...

Authors: Md Mansur Alam, Shruti Dubey and Dumitru Baleanu

Bifurcation curves and exact multiplicity of positive solutions for Dirichlet problems with the Minkowski-curvature equation

In this paper, we consider the bifurcation curves and exact multiplicity of positive solutions of the one-dimensional Minkowski-curvature equation

Authors: Hongliang Gao and Jing Xu

A weak solution for a \((p(x),q(x))\)-Laplacian elliptic problem with a singular term

Authors: MirKeysaan Mahshid and Abdolrahman Razani

Multiple solutions for singular semipositone boundary value problems of fourth-order differential systems with parameters

The aim of this paper is to establish some results about the existence of multiple solutions for the following singular semipositone boundary value problem of fourth-order differential systems with parameters:

Authors: Longfei Lin, Yansheng Liu and Daliang Zhao

Multiple solutions for a quasilinear Schrödinger–Poisson system

Authors: Jing Zhang

Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

A nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

Authors: Abdelbaki Choucha and Salah Boulaaras

Radial solutions for fully nonlinear elliptic equations of Monge–Ampère type

First, the symmetry of classical solutions to the Monge–Ampère-type equations is obtained by the moving plane method. Then, the existence and nonexistence of radial solutions in a ball are got from the symmetr...

Authors: Limei Dai, Huihui Cheng and Hongfei Li

Effect of the protection zone in a diffusive ratio-dependent predator–prey model with fear and Allee effect

In this paper, we study the influence of a protection zone for the prey on a diffusive predator–prey model with fear factor and Allee effect. The prior estimate, global existence, nonexistence of nonconstant p...

Authors: Huan Wang and Hui Xing

Existence of solutions for a class of Kirchhoff-type equations with indefinite potential

Authors: Jian Zhou and Yunshun Wu

A fractional differential equation with multi-point strip boundary condition involving the Caputo fractional derivative and its Hyers–Ulam stability

In this work, we investigate the existence, uniqueness, and stability of fractional differential equation with multi-point integral boundary conditions involving the Caputo fractional derivative. By utilizing ...

Authors: Mehboob Alam, Akbar Zada, Ioan-Lucian Popa, Alireza Kheiryan, Shahram Rezapour and Mohammed K. A. Kaabar

A note on global existence of strong solution to the 3D micropolar equations with a damping term

Authors: Wen Wang and Yunchong Long

Existence and uniqueness of a finite energy solution for the mixed value problem of porous thermoelastic bodies

We consider the mixed problem with boundary and initial data in thermoelasticity of porous bodies with dipolar structure. By generalizing some known results developed by Dafermos in a more simple case of the c...

Authors: M. Marin, S. Vlase and C. Carstea

Well posedness of a nonlinear mixed problem for a parabolic equation with integral condition

The aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and ...

Authors: Abdelkader Djerad, Ameur Memou and Ali Hameida

On Green’s function of Cauchy–Dirichlet problem for hyperbolic equation in a quarter plane

The definition of a Green’s function of a Cauchy–Dirichlet problem for the hyperbolic equation in a quarter plane is given. Its existence and uniqueness have been proven. Representation of the Green’s function...

Authors: Makhmud Sadybekov and Bauyrzhan Derbissaly

Nonlocal Lazer–McKenna-type problem perturbed by the Hardy’s potential and its parabolic equivalence

In this paper, we study the effect of Hardy potential on the existence or nonexistence of solutions to the following fractional problem involving a singular nonlinearity:

Authors: Masoud Bayrami-Aminlouee, Mahmoud Hesaaraki, Mohamed Karim Hamdani and Nguyen Thanh Chung

Some properties of implicit impulsive coupled system via φ-Hilfer fractional operator

The major goal of this work is investigating sufficient conditions for the existence and uniqueness of solutions for implicit impulsive coupled system of φ-Hilfer fractional differential equations (FDEs) with ins...

Authors: Mohammed A. Almalahi and Satish K. Panchal

Nonlinear differential equations with perturbed Dirichlet integral boundary conditions

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied probl...

Authors: Alberto Cabada and Javier Iglesias

Retraction Note: New applications of Schrödingerean Green potential to boundary behaviors of superharmonic functions

Authors: Kai Lai, Jing Mu and Hong Wang

Implicit nonlinear fractional differential equations of variable order

In this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to...

Authors: Amar Benkerrouche, Mohammed Said Souid, Kanokwan Sitthithakerngkiet and Ali Hakem

Blow-up for a viscoelastic von Karman equation with strong damping and variable exponent source terms

In this article, we deal with a strongly damped von Karman equation with variable exponent source and memory effects. We investigate blow-up results of solutions with three levels of initial energy such as non...

Authors: Sun-Hye Park

A new blow up criterion for the 3D magneto-micropolar fluid flows without magnetic diffusion

This note obtains a new regularity criterion for the three-dimensional magneto-micropolar fluid flows in terms of one velocity component and the gradient field of the magnetic field. The authors prove that the...

Authors: Dongxiang Chen and Qifeng Liu

A blow-up result for a system of coupled viscoelastic equations with arbitrary positive initial energy

This article is devoted to a study of the blow-up result for a system of coupled viscoelastic wave equations. By establishing a new auxiliary function and using the reduction to absurdity method, we obtain som...

Authors: Qian Li

Three new approaches for solving a class of strongly nonlinear two-point boundary value problems

Three new and applicable approaches based on quasi-linearization technique, wavelet-homotopy analysis method, spectral methods, and converting two-point boundary value problem to Fredholm–Urysohn integral equa...

Authors: Monireh Nosrati Sahlan and Hojjat Afshari