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Radial solutions for nonlinear elliptic equation with nonlinear nonlocal boundary conditions

Kossowski Igor

Opuscula Mathematica

2023

Vol. 43, no. 5

675--687

In this article, we prove existence of radial solutions for a nonlinear elliptic equation with nonlinear nonlocal boundary conditions. Our method is based on some fixed point theorem in a cone.

The radial solution of the heat equation in the cylindrical ring

Koroński J.

Fasciculi Mathematici

2010

Nr 43

69-83

The subject of the paper is the construction of a solution to the parabolic problem for the cylindrical ring with initial condition of Cauchy type and boundary conditions of Dirichlet type. To construct the radial solution we do not use the Bessel functions but we apply the convenient Green function, heat potentials and Banach fixed point theorem.

On boundary value problem for a nonlocal elliptic equation

Fijałkowski P., Przeradzki B.

Journal of Applied Analysis

2003

Vol. 9, nr 2

201-209

The existence of a positive radial solution to the Dirichlet boundary value problem for the second order elliptic equation [wzór], where U = B(0, R) \ ‾B(0, ρ), with weak assumptions on the nonlinear term f, is proved. The method based on the Krasnosel'skii Fixed Point Theorem enables to find many solutions to the problem. Solutions for the same problem but with U = B(0, R) and with nonlinear term f depending explicitely on |x| are found as well.