相关论文: Nonlinear differential equations on non-compact do…

We prove the existence of non-smooth solutions to fully nonlinear uniformly elliptic equations.

We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…

New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…

We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…

In this paper, we study a broad class of fully nonlinear elliptic equations on Hermitian manifolds. On one hand, under the optimal structural assumptions we derive $C^{2,\alpha}$-estimate for solutions of the equations on closed Hermitian…

The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…

Inspired by the penalization of the domain approach of Lions & Sznitman, we give a sense to Neumann and oblique derivatives boundary value problems for nonlocal, possibly degenerate elliptic equations. Two different cases are considered:…

In this note, we review the latest qualitative results, referring to the Li\'enard Equation, in the framework of non-conformable, generalized and fractional differential operators.

On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.

The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…

We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many…

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in [Ann. Phys. 351, 1-12 (2014)]. The exact solutions of these equations give the number…

We consider an oblique derivative problem for non-divergence parabolic equations with discontinuous in $t$ coefficients in a half-space. We obtain weighted coercive estimates of solutions in anisotropic Sobolev spaces. We also give an…

This article is concerned with the nonexistence of positive solutions for nonlinear fractional elliptic inequalities in exterior domains of $\mathbb R^n$, $n\geq1$. We would like to highlight the fact that our results are new with very weak…

We show existence and uniqueness results for nonlinear parabolic equations in noncylindrical domains with possible jumps in the time variable

We survey recent results on the control problem for the heat equation on unbounded and large bounded domains. First we formulate new uncertainty relations, respectively spectral inequalities. Then we present an abstract control cost…

In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…

In this paper we discuss the extention of MPE methods to nonlinear differential equations. We concentrate on nonlinear systems of differential equations and generalize the recent MPE method, see the work of Chin and Geiser 2010.

In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of…