Existence and uniqueness theorems for semilinear elliptic boundary value problems

Kazuaki Taira

Abstract

This paper is devoted to the study of a class of degenerateboundary value problems for semilinear second-order elliptic differential operators depending nonlinearly on $\nabla u$. The purpose of this paper is to prove existence and uniqueness theorems of solutions of semilinear elliptic boundary value problems, by making use of the super-subsolution method and the Leray-Schauder degree theory. We remark that the variational method approach would fail, since our boundary condition is degenerate.

Article information

Source
Adv. Differential Equations, Volume 2, Number 4 (1997), 509-534.

Dates
First available in Project Euclid: 23 April 2013

Mathematical Reviews number (MathSciNet)
MR1441854

Zentralblatt MATH identifier
1023.35510

Citation

Taira, Kazuaki. Existence and uniqueness theorems for semilinear elliptic boundary value problems. Adv. Differential Equations 2 (1997), no. 4, 509--534. https://projecteuclid.org/euclid.ade/1366741146