Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 428, Issue 1, Pages 696-712Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2015.03.033
Keywords
Quasilinear elliptic equations; Resonant; Morse theory
Categories
Funding
- BNSF [1132012]
- NSFC [61272026, 11271264, 11301010]
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In this paper, by Morse theory we will compute the critical groups at zero for a functional I : W-0(1,p)(Omega) -> R defined by setting I(u) = 1/p integral(Omega)vertical bar del u vertical bar(p)dx+1/2 integral(Omega)vertical bar del u vertical bar(2)dx- integral F-Omega(x,u)dx, where p> 2, Omega is a bounded domain in R-N, F(x,u) = integral(u)(0) f(x,t)dt and we assume that f is resonant at zero for the spectrum of -Delta in W-0(1,2)(Omega). As an application of these critical groups estimates, some multiplicity results are also given. (C) 2015 Elsevier Inc. All rights reserved.
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