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Indexed by:Journal Papers

Date of Publication:2020-01-01

Journal:ADVANCES IN NONLINEAR ANALYSIS

Included Journals:SCIE

Volume:9

Issue:1

Page Number:1420-1436

ISSN No.:2191-9496

Key Words:Quasilinear elliptic equation; Positive solution; Nehari manifold

Abstract:We are concerned with the following quasilinear elliptic equation
   -Delta u -Delta(u(2))u =mu vertical bar u vertical bar(q-2)u +vertical bar u vertical bar(2.2*-2)u, u is an element of H-0(1)(Omega), (QSE)
   where Omega subset of R-N is a bounded domain, N >= 3, q(N) < q < 2.2* , 2* = 2N/(N- 2), q(N) = 4 for N >= 6 and q(N) = 2(N+2)/N-2 for N = 3, 4, 5, and y is a positive constant. By employing the Nehari manifold and the Lusternik-Schnirelman category theory, we prove that there exists mu* > 0 such that (QSE) admits at least cat(Omega)(Omega) positive solutions when mu is an element of (0, mu*).