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This paper focuses on the problem of noise removal. First, we propose a new convex–nonconvex variation model for noise removal and consider the nonexistence of solutions of the variation model. Based on the ne...
The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary c...
By using variational methods we obtain infinitely many nontrivial solutions for a class of nonperiodic Schrödinger lattice systems, where the nonlinearities are sublinear at both zero and infinity.
In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the he...
The main goal of this paper is investigating the existence of nonconstant positive steady states of a linear prey–predator cross-diffusion system with Beddington–DeAngelis and Tanner functional response. An an...
In this paper, we investigate a delay reaction–diffusion–advection model with ideal free dispersal. The stability of positive steady-state solutions and the existence of the associated Hopf bifurcation are obt...
In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain t...
This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform
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Results reported in this paper study the existence and stability of a class of implicit generalized proportional fractional integro-differential Langevin equations with nonlocal fractional integral conditions....
In our paper we address the thermoelasticity theory of the strain gradient. First, we define the mixed problem with initial and boundary data in this context. Then, with the help of an identity of Lagrange typ...
In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerki...
The paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. ...
In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the...
This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumpti...
The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional deriv...
This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, ...
This work is devoted to investigating the local well-posedness for an integrable evolution equation and behaviors of its solutions, which possess blow-up criteria and persistence property. The existence and un...
By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functi...
In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theo...
This paper considered the spectral meshless radial point interpolation (SMRPI) method to unravel for the nonlinear p-Laplacian equation with mixed Dirichlet and Neumann boundary conditions. Through this assessmen...
This article has been retracted. Please see the retraction notice for more detail: https://​doi.​org/​10.​1186/​s13661-015-0363-z.
The original article was published in Boundary Value Problems 2015 2015:114
In this paper, we consider the three-dimensional compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition in a bounded smooth domain. The main idea is to deri...
In this paper, we present a theorem for some impulsive boundary problems with derivative dependence by the upper and lower solutions method. Using the theorem obtained, we consider the existence of positive so...
The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the qu...
In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficie...
We consider a nonlinear Dirichlet problem driven by a general nonhomogeneous differential operator and with a reaction exhibiting the combined effects of a parametric singular term plus a Carathéodory perturba...
In this work, we propose a nonstationary Navier–Stokes problem equipped with an unusual boundary condition. The time discretization of such a problem is based on the backward Euler’s scheme. However, the varia...
Sun and Ma (J. Differ. Equ. 255:2534–2563, 2013) proved the existence of a nonzero T-periodic solution for a class of one-dimensional lattice dynamical systems,
...In this paper we study the self-improving property of the obstacle problem related to the singular porous medium equation by using the method developed by Gianazza and Schwarzacher (J. Funct. Anal. 277(12):1–57,
In this paper, we deal with a class of fractional critical problems. Under some suitable assumptions, we derive the existence of a positive solution concentrating at the critical point of the Robin function by...
This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the...
In this paper, we introduce and study a tripled system of three associated fractional differential equations. Prior to proceeding to the main results, the proposed system is converted into an equivalent integr...
It is difficult to exactly and automatically satisfy nonseparable multipoint boundary conditions by numerical methods. With this in mind, we develop a novel algorithm to find solution for a second-order nonlin...
In this research article, we develop a qualitative analysis to a class of nonlinear coupled system of fractional delay differential equations (FDDEs). Under the integral boundary conditions, existence and uniq...
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