Duong Minh Duc, Loc Hoang Nguyen, Luc Nguyen
Abstract:
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 email: dmduc@hcmuns.edu.vn | |
Loc Hoang Nguyen Department of Mathematics, Ecole Normale Suprieure Paris, France email: lnguyen@dma.ens.fr | |
lu Nguyen Department of Mathematics, Princeton University Princeton, New Jersey 08544, USA email: llnguyen@princeton.edu |
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