相关论文: Existence of solution for Hilfer fractional differ…
This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The…
Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains with prescribed conditions on the complement of the domain. Our main focus is on the inhomogeneous Neumann problem in a rather general setting. We also…
We investigate the existence of solutions of constrained nonlinear differential inclusions with nonlocal boundary conditions. Our viability theorems are based on the assumption that the right-hand side of differential inclusion is defined…
We study boundary regularity for the inhomogeneous Dirichlet problem for $2s$-stable operators in generalized H\"older spaces. Moreover, we provide explicit counterexamples that showcase the sharpness of our results. Our approach directly…
In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point…
We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.
We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric singular kernel. We define a notion of weak solution adapted to…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…
We study the existence of positive solutions for a parameter-dependent nonlocal boundary value problem involving a Caputo fractional derivative, which generalizes a classic thermostat model. Our approach extends previous work by considering…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators…
In this paper, we investigate the existence of mild solutions to Hilfer fractional equation of semi-linear evolution with non-instantaneous impulses, using the concepts of equicontinuous $C_{0}$-semigroup and Kuratowski measure of…
In this article, we consider the boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence…
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
By means of classical fixed point index, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations where the nonlinearities are allowed to…
We study generalized fractional $p$-Laplacian equations to prove local boundedness and H\"older continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincar\'e inquality.
We begin by proving a local existence result for a fractional Caputo nonlocal thermistor problem. Then, additional existence and continuation theorems are obtained, ensuring global existence of solutions.
In this paper we study an equation driven by a nonlocal anisotropic operator with homogeneous Dirichlet boundary conditions. We find at least three non trivial solutions: one positive, one negative and one of unknown sign, using variational…
This work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass…