Multiplicity of positive solutions for a semilinear elliptic equationin $R_+^N$ with nonlinear boundary condition

Tsung-Fang Wu

doi:10.3934/cpaa.2010.9.1675

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2010, Volume 9, Issue 6: 1675-1696. Doi: 10.3934/cpaa.2010.9.1675

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Multiplicity of positive solutions for a semilinear elliptic equation in $R_+^N$ with nonlinear boundary condition

Tsung-Fang Wu^1,

1.
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811

Received: July 31, 2009

Revised: January 31, 2010

Published: October 2010

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Abstract

In this paper, we study a class of semilinear elliptic equations in $R_+^N$ with nonlinear boundary condition and sign-changing weight function. By means of the Lusternik-Schnirelman category, multiple positive solutions are obtained.

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Mathematics Subject Classification: Primary: 35J50, 35J55; Secondary: 35J65.

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Multiplicity of positive solutions for a semilinear elliptic equation in $R_+^N$ with nonlinear boundary condition

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