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In this paper, some Banach spaces are introduced. Based on these spaces and the coincidence degree theory, a 2m-point boundary value problem for a coupled system of impulsive fractional differential equations ...
In this paper, we obtain the existence of multiple positive solutions of a boundary value problem for α-order nonlinear integro-differential equations in a Banach space by means of fixed point index theory of com...
In this paper, the existence and blow-up property of solutions to an initial and boundary value problem for a nonlinear parabolic system with variable exponents is studied. Meanwhile, the blow-up property of s...
In recent years attention has been directed to the problem of solving the Poisson equation, either in engineering scenarios (computational) or in regard to crystal structure (theoretical).
In this paper, we make use of a new stability result and bifurcation theory to study the existence and uniqueness of positive solutions to semilinear elliptic systems with some general sublinear conditions. Mo...
We study a driven sixth-order Cahn-Hilliard type equation which arises naturally as a continuum model for the formation of quantum dots and their faceting. Based on the Leray-Schauder fixed point theorem, we p...
The aim of this work is to study adaptive fully-discrete finite element methods for quadratic boundary optimal control problems governed by nonlinear parabolic equations. We derive a posteriori error estimates fo...
We approximate impact systems in arbitrary finite dimensions with fast-slow dynamics represented by regular ODE on one side of the impact manifold and singular ODE on the other. Lyapunov-Schmidt method leading...
In this paper, it is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on generalized Morrey spaces
...
In this paper, the author discusses the multiple positive solutions for an infinite three-point boundary value problem of first-order impulsive superlinear singular integro-differential equations on the half l...
We develop a formulation for the analytic or approximate solution of fractional differential equations (FDEs) by using respectively the analytic or approximate solution of the differential equation, obtained b...
In this short note we study a simple discrete Fučík spectrum. Trying to imitate standard continuous pasting procedures, we derive a more complicated discrete analogue - anchoring. Using this technique, we show...
Near an equilibrium we study the existence of asymptotically a.p. (almost periodic), asymptotically a.a. (almost automorphic), pseudo a.p., pseudo a.a., weighed pseudo a.p. and weighed pseudo a.a. solutions of...
The sampling theory says that a function may be determined by its sampled values at some certain points provided the function satisfies some certain conditions. In this paper we consider a Dirac system which c...
In this paper, we study some properties of the generalized Apostol-type polynomials (see (Luo and Srivastava in Appl. Math. Comput. 217:5702-5728, 2011)), including the recurrence relations, the differential e...
We put forward the notion of unconditional convergence to an equilibrium of a difference equation. Roughly speaking, it means that can be constructed a wide family of higher order difference equations, which inhe...
In this article, a new homotopy technique is presented for the mathematical analysis of finding the solution of a first-order inhomogeneous partial differential equation (PDE) ...
The Erratum to this article has been published in Boundary Value Problems 2015 2015:72
A semilinear multivalued evolution equation is considered in a reflexive Banach space. The nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second...
In this paper, we obtain some circular summation formulas of theta functions using the theory of elliptic functions and show some interesting identities of theta functions and applications.
In this paper, a regularity criterion for the 3D magneto-micropolar fluid equations is investigated. A sufficient condition on the derivative of the velocity field in one direction is obtained. More precisely,...
For a constructive analysis of the periodic boundary value problem for systems of non-linear non-autonomous ordinary differential equations, a numerical-analytic approach is developed, which allows one to both...
In this paper, we investigate some new identities related to the unification of the Bernstein-type polynomials, Bernoulli polynomials, Euler numbers and Stirling numbers of the second kind. We also give some r...
In the present paper, in view of the variational approach, we discuss a Ni-Serrin type equation involving non-standard growth condition and arising from the capillarity phenomena. Establishing some suitable co...
In this paper we propose a new method for solving the mixed boundary value problem for the Laplace equation in unbounded multiply connected regions. All simple closed curves making up the boundary are divided ...
In this paper, the groundwater flow equation is generalized using the concept of the variational order derivative. We present a numerical solution of the modified groundwater flow equation with the variational...
In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that...
In this paper, abstract results concerning the approximate controllability of semilinear evolution systems in a separable reflexive Banach space are obtained. An approximate controllability result for semiline...
In this paper, we are concerned with an inverse problem for the Sturm-Liouville operator with Coulomb potential using a new kind of spectral data that is known as nodal points. We give a reconstruction of q as a ...
The magnetohydrodynamic stability criterion of self-gravitating streaming fluid cylinder under the combined effect of self-gravitating, magnetic, and capillary forces has been derived. The results are discusse...
Sufficient conditions are established guaranteeing the existence of a positive ω-periodic solution to the equation
The aim of this paper is to give not only the matrix representation of partial Hecke-type operators by means of Bernoulli polynomials and Euler polynomials, but also functional equations and differential equat...
We discuss the one-sided Green’s function, associated with an initial value problem and the two-sided Green’s function related to a boundary value problem. We present a specific calculation associated with a d...
In this paper, we investigate extinction properties of the solutions for the initial Dirichlet boundary value problem of a porous medium equation with nonlocal source and strong absorption terms. We obtain som...
The purpose of the present paper is to investigate some strong differential subordination and superordination implications involving the Komatu integral operator which are obtained by considering suitable clas...
This article presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient
In this paper we study the initial-boundary value problem of the multidimensional viscoelasticity equation with nonlinear source term
The main objective of this paper is to study the fractional Hankel transformation and the continuous fractional Bessel wavelet transformation and some of their basic properties. Applications of the fractional ...
An analysis is carried out to study the heat transfer characteristics of steady two-dimensional stagnation-point flow of a copper (Cu)-water nanofluid over a permeable stretching/shrinking sheet. The stretchin...
In this paper, we study three-point boundary value problems of the following fractional functional differential equations involving the Caputo fractional derivative:
Based on the fixed point index and partial order method, one new order-type existence theorem concerning cone expansion and compression is established. As applications, we present sufficient existence conditio...
Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. In this paper we use the derivative s...
In this paper, we investigate the complicated asymptotic behavior of the solutions to the Cauchy problem of a porous medium equation with nonlinear sources when the initial value belongs to a weighted
In this article, we study the periodic solution of a quasilinear parabolic equation with nonlocal terms and Neumann boundary conditions. By using the theory of Leray-Schauder degree, we obtain the existence of...
In this work, we discuss Riemann-Hilbert and its adjoint homogeneous problem associated with generalized Q-holomorphic functions and investigate the solvability of the Riemann-Hilbert problem.
In this paper, the problem of magnetohydrodynamic (MHD) flow of a viscous fluid on a nonlinear porous shrinking sheet is studied. The boundary layer partial differential equations are first transformed into an...
In the present paper, we consider the abstract Cauchy problem for the fractional differential equation
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