Duong Minh Duc, Loc Hoang Nguyen, Luc Nguyen
We study the multiplicity of solutions to the elliptic equation , under the assumption that f(x,u)/u crosses globally but not pointwise any eigenvalue for every x in a part of the domain, when u varies from to . Also we relax the conditions on uniform convergence of f(x,s)/s, which are essential in many results on multiplicity for asymptotically linear problems.
Submitted April 10, 2013. Published June 25, 2013.
Math Subject Classifications: 47H11, 55M25, 35J20.
Key Words: Index of critical points; mountain pass type; nonlinear elliptic equations; multiplicity of solutions.
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| Duong Minh Duc |
University of Sciences - Hochiminh City, Vietnam
| Loc Hoang Nguyen |
Department of Mathematics, Ecole Normale Suprieure
| lu Nguyen |
Department of Mathematics, Princeton University
Princeton, New Jersey 08544, USA
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