TY: JOUR
T1 - Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
A1 - Aizicovici, S.
A1 - Papageorgiou, N. S.
A1 - Staicu, V.
N2 - We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ?concave? (i.e., (p ? 1)? sublinear) near zero and
?convex? (i.e., (p ? 1)? superlinear) near ±1. Using variational methods combined with truncation
and comparison techniques, we show that for all small values of the parameter > 0, the problem
has at least five nontrivial smooth solutions (four of constant sign and the fifth nodal). In the Hilbert
space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its sign.
UR - https://ria.ua.pt/handle/10773/14988
Y1 - 2015
PB - International Press