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In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.
In the given article the necessary and sufficient conditions of the existence of solutions of boundary value problem for the nonlinear system in the Hilbert spaces are obtained. Examples of such systems like a Lotka-Volterra are considered.…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
In the article, some bilinear evolution equations in Hilbert space driven by paths of low regularity are considered and solved explicitly. The driving paths are scalar-valued and continuous, and they are assumed to have a finite $p$-th…
Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
In this paper we analyse some possibilities of finding positive solutions for second order boundary value problems with Dirichlet and periodic boundary conditions, for which the correspondent Green's functions change sign. The obtained…
In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…
We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for…
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the…
It is shown that the non-homogeneous Dirichlet and Neuman problems for the $2^{nd}$-order Seiberg-Witten equation admit a regular solution once the $\mathcal{H}$-condition (described in the article) is satisfied. The approach consist in…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…
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
Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…