TY: JOUR
T1 - Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations
A1 - Aizicovici, S.
A1 - Papageorgiou, N. S.
A1 - Staicu, Vasile
N2 - We consider nonlinear, nonhomogeneous Dirichlet problems driven
by the sum of a p?Laplacian (p > 2) and a Laplacian, with a reaction term
which has space dependent zeros of constant sign. We prove three muliplicity
theorems for such equations providing precise sign information for all solutions.
In the first multiplicity theorem, we do not impose any growth condition on
the reaction near ±?: In the other two, we assume that the reaction is (p ? 1)?
linear and resonant with respect to principal eigenvalue of
(
??p;W1,p
0 (?)
)
: Our
approach uses variational methods based on the critical point theory, together
with suitable truncation and comparison techniques and Morse theory (critical
groups).
UR - https://ria.ua.pt/handle/10773/18726
Y1 - 2014
PB - Yokohama Publishers