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Multiple nontrivial solutions for nonlinear eigenvalue problems
Author(s):
D.
Motreanu;
V.
V.
Motreanu;
N.
S.
Papageorgiou
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3649-3658.
MSC (2000):
Primary 35J60;
Secondary 35J70
Posted:
August 7, 2007
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Additional information
Abstract:
In this paper we study a nonlinear eigenvalue problem driven by the  -Laplacian. Assuming for the right-hand side nonlinearity only unilateral and sign conditions near zero, we prove the existence of three nontrivial solutions, two of which have constant sign (one is strictly positive and the other is strictly negative), while the third one belongs to the order interval formed by the two opposite constant sign solutions. The approach relies on a combination of variational and minimization methods coupled with the construction of upper-lower solutions. The framework of the paper incorporates problems with concave-convex nonlinearities.
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Additional Information:
D.
Motreanu
Affiliation:
Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France
Email:
motreanu@univ-perp.fr
V.
V.
Motreanu
Affiliation:
Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France
Email:
viorica@univ-perp.fr
N.
S.
Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Athens 15780, Greece
Email:
npapg@math.ntua.gr
DOI:
10.1090/S0002-9939-07-08927-7
PII:
S 0002-9939(07)08927-7
Keywords:
Nonlinear eigenvalue problem,
$p$-Laplacian,
principal and second eigenvalue,
upper-lower solution,
truncation,
strong maximum principle,
second deformation lemma
Received by editor(s):
August 1, 2006
Received by editor(s) in revised form:
September 6, 2006
Posted:
August 7, 2007
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
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