Artículos de revistas
SUPERLINEAR ELLIPTIC PROBLEMS WITH SIGN CHANGING COEFFICIENTS
Date
2013-08-02Registration in:
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, SINGAPORE, v. 14, n. 1, pp. 1250001-1-1250001-21, FEB, 2012
0219-1997
10.1142/S0219199712500010
Author
Massa, Eugenio Tommaso
Ubilla, Pedro
Institutions
Abstract
Via variational methods, we study multiplicity of solutions for the problem {-Delta u = lambda b(x)vertical bar u vertical bar(q-2)u + au + g(x, u) in Omega, u - 0 on partial derivative Omega, where a simple example for g( x, u) is |u|(p-2)u; here a, lambda are real parameters, 1 < q < 2 < p <= 2* and b(x) is a function in a suitable space L-sigma. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any lambda > 0, and a total of five nontrivial solutions are obtained when lambda is small and a >= lambda(1). Note that this type of results are valid even in the critical case.