Differential and Integral Equations

Multiple solutions for semilinear elliptic systems involving critical Sobolev exponent

Michinori Ishiwata

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The effect of the domain topology on the multiplicity of solutions for a semilinear elliptic system with critical Sobolev exponent is discussed. We show that if the coupling term is sufficiently small, then there exist at least cat $\Omega$ positive solutions, where cat denotes the Ljusternik-Schnirelman category.

Article information

Differential Integral Equations, Volume 20, Number 11 (2007), 1237-1252.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J55
Secondary: 35B33: Critical exponents 35J50: Variational methods for elliptic systems 35J60: Nonlinear elliptic equations 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space


Ishiwata, Michinori. Multiple solutions for semilinear elliptic systems involving critical Sobolev exponent. Differential Integral Equations 20 (2007), no. 11, 1237--1252. https://projecteuclid.org/euclid.die/1356039287

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