Related papers: Positive solutions of BVPs on the half-line involv…
Boundary conditions (BCs) are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations (PDEs) to satisfy at specific spatial locations. These constraints carry important physical…
The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
The existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. The fourth-order radial equation is non-self adjoint and has no exact solutions.…
We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a…
We formulate on rectangles and on the right horizontal half-strip initial-boundary value problems for a two-dimensional Benney-Lin type equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the…
We prove new results on the existence of positive solutions for some impulsive differential equation subject to nonlocal boundary conditions. Our boundary conditions involve an affine functional given by a Stieltjes integral. These cover…
We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem,…
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…
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…
The existence of multiple fixed points for the coercive, bilinear, compact forms defined in the cone in the Banach space. Multiple applications to the integral equations derived from BVPs for differential equations are provided.
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
We discuss the existence of eigenvalues for a third order boundary value problem subject to functional boundary conditions and higher order derivative dependence in the nonlinearities. We prove the existence of positive and negative…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
The existence of at least two solutions to superlinear integral equation in cone is proved using the Krasnosielskii Fixed Point Theorem. The result is applied to the Dirichlet BVPs with the fractional Laplacian.
The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and…