Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition

Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition

Numerical solution of nonlinear elliptic equation with nonlocal condition ∗

Regimantas Čiupaila, Mifodijus Sapagovas, Olga Štikonienė Vilnius Gediminas Technical University Saulėtekio ave. 11, LT-10223 Vilnius, Lithuania [email protected] Institute of Mathematics and Informatics, Vilnius University Akademijos str. 4, LT-08663 Vilnius, Lithuania [email protected] Vilnius University Naugarduko str. 24, LT-03225 Vilnius, Lithuania olga.stikoniene@mif...

The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition

Abstract. We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition −∂u/∂νA = g(·, ·, u) with a locally defined, Lr-bounded function g(t, ·, ξ). We prove the existence of a local weak solution to the problem by means of ...

Blow up problems for a degenerate parabolic equation with nonlocal source and nonlocal nonlinear boundary condition

* Correspondence: zhgs917@163. com Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and globa...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.