Indexed by:
Journal Papers
First Author:
Fang, Xiangdong
Correspondence Author:
Fang, XD (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.
Co-author:
Zhang, Jianjun
Date of Publication:
2020-01-01
Journal:
ADVANCES IN NONLINEAR ANALYSIS
Included Journals:
SCIE
Document Type:
J
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*).
Translation or Not:
no
