Open AccessStrongly indefinite functionals and multiple solutions of elliptic systems
Author(s) -
D. De Figueiredo,
Yanheng Ding
Publication year - 2003
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-03-03257-4
Subject(s) - parenthesis , algorithm , mathematics , philosophy , linguistics
We study existence and multiplicity of solutions of the elliptic system (GRAPHICS) where Omega subset of R-N; Ngreater than or equal to3, is a smooth bounded domain and His an element ofC(1) ((Omega) over barx R-2, R). We assume that the nonlinear term (GRAPHICS) where p is an element of (1, 2*), 2* := 2N/(N-2), and q is an element of (1,infinity). So some supercritical systems are included. Nontrivial solutions are obtained. When H(x, u, v) is even in (u, v), we show that the system possesses a sequence of solutions associated with a sequence of positive energies (resp. negative energies) going toward infinity (resp. zero) if p>2 (resp. p<2). All results are proved using variational methods. Some new critical point theorems for strongly indefinite functionals are proved