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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.

Solvability conditions for a nonlocal boundary value problem for linear functional differential equations

Lomtatidze A., Opluštil Z., Šremr J.

Fasciculi Mathematici

2009

Nr 41

81-96

On the nonlocal boundary value problem for first order quasilinear partial functional differential equations

Człapiński T.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

57-73

Quasilinear partial functional differential equations of the first order with nonlocal boundary condi-tions are considered. A theorem on the local existence and uniqueness of classical solutions is given. The method of bicharacteristics is used to transform the nonlocal boundary value problem into a functional integral equation and the Banach fixed-point principle to find its solution.