Advances in Differential Equations

Existence and uniqueness theorems for semilinear elliptic boundary value problems

Kazuaki Taira

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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

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

First available in Project Euclid: 23 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations


Taira, Kazuaki. Existence and uniqueness theorems for semilinear elliptic boundary value problems. Adv. Differential Equations 2 (1997), no. 4, 509--534.

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