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Positive Solutions for a Class of p-q-Laplacian Type Equations with Potentials in RN

Volume 2, Number 2 (2012), 93 - 109

Positive Solutions for a Class of p-q-Laplacian Type Equations with Potentials in RN

Communicated By: 
Enrique Zuazua
Price: $20.00

Abstract

We study the nonlinear equation −div(|ru|p−2ru)−div(|ru|q−2ru)+1a(x)|u|p−2u+2b(x)|u|q−2u = μ1|u|p−2u+1|u|p−2u+μ2|u|q−2u+2|u|q−2u where u 2 RN with critical exponent p = pN/(N − p), q = qN/(N −q), N > p q 2, N > 3, where a 0 and b 0 has a potential well. Using variational methods, we obtain existence and multiplicity of positive solutions which localize near the potential well for μ1, μ2, 1, 2 small and 1, 2 large.