Related papers: Solvability of a sixth-order boundary value proble…

The Schr\"odinger equation is considered on the half line with a selfadjoint boundary condition when the potential is real valued, integrable, and has a finite first moment. It is proved that the potential and the two boundary conditions…

In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…

In this paper we are interested in obtaining the exact expression and the study of the constant sign of the Green's function related to a second order perturbed periodic problem coupled with integral boundary conditions at the extremes of…

The purpose of this paper is to investigate some spectral properties of Sturm-Liouville type problems with interior singularities. Some of the mathematical aspects necessary for developing own technique presented. By applying this technique…

In this paper we study the $5$th Order Kadomstev-Petviashvili (KP) equations posed on the real line. In particular we adapt the energy estimate argument from Guo-Molinet (arXiv:2404.12364v1 [math.AP]) to conclude unconditional uniqueness of…

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…

In this paper, we consider the Laplace equation with a class of indefinite superlinear boundary conditions and study the uniqueness of positive solutions that this problem possesses. Superlinear elliptic problems can be expected to have…

A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…

The main purpose of this paper is to establish the existence, nonexistence and symmetry of nontrivial solutions to the higher order Brezis-Nirenberg problems associated with the GJMS operators $P_k$ on bounded domains in the hyperbolic…

We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption…

In this article, we prove an existence of solutions for a non-local boundary value problem with nonlinearity in a nonlocal condition. Our method is based upon the Mawhin's coincidence theory.

Necessary and sufficient conditions for existence of boundary value problem of Schrodinger equation are obtained in linear and nonlinear cases. Periodic analytical solutions are represented using generalized Green's operator

The purpose of this paper is to make a few connections among specific concepts occurring in differential geometry and the theory of differential equations with the aim of identifying an intriguing class of undetermined nonlinear ordinary…

This paper concerns a second-order differential equation with indefinite and repulsive singularities. It is the first time to study differential equation containing both indefinite and repulsive singularities simultaneously. A set of…

We discuss, via a version of the Birkhoff-Kellogg theorem, the existence of positive and negative eigenvalues of Hammerstein integral equations with sign-changing nonlinearities and functional terms. The corresponding eigenfunctions have a…

The equation arising from Prandtl boundary layer theory is considered. The existence of the entropy solution can be proved by BV estimate method. The interesting problem is that, since a may be degenerate on the boundary, the usual boundary…

This paper establishes a Lyapunov-type inequality for a class of fractional boundary value problems (BVPs) involving two Hadamard fractional derivatives of different orders with Dirichlet boundary conditions. The method is based on the…

This paper is concerned with a class of nonlinear boundary value problem involving fractional derivative in the $\varphi$-Riemann-Liouville sense. Some Properties of the Green's function for this problem are mentioned. By means of the…

The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…