Electron. J. Diff. Eqns., Vol. 2005(2005), No. 57, pp. 112.
A multiplicity result for quasilinear problems with
convex and concave nonlinearities and nonlinear
boundary conditions in unbounded domains
Dimitrios A. Kandilakis
Abstract:
We study the following quasilinear problem with nonlinear boundary
conditions
where
is an unbounded domain in
with a noncompact and smooth boundary
,
denotes
the unit outward normal vector on
,
is the
Laplacian,
,
,
and
are nonnegative essentially
bounded functions,
and
. The properties of the first eigenvalue
and the associated eigenvectors of the
related eigenvalue problem are examined. Then it is shown that if
,
the original problem admits an infinite
number of solutions one of which is nonnegative, while if
it admits at least one nonnegative solution.
Our approach is variational in character.
Submitted September 27, 2004. Published May 31, 2005.
Math Subject Classifications: 35J20, 35J60.
Key Words: Variational method; fibering method;
PalaisSmale condition; genus.
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Dimitrios A. Kandilakis
Department of Sciences
Technical University Of Crete
Chania, Crete, 73100 Greece
email: dkan@science.tuc.gr 
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