Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities. (English) Zbl 1322.35036 Methods Appl. Anal. 22, No. 2, 221-248 (2015). The authors study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is \(p-1\)-sublinear near zero and \(p-1\)-superlinear near \(\pm\infty\). The existence of at least five nontrivial smooth solutions for small values of the parameter is shown; four of them have constant sign and the fifth is nodal. In a special case of Hilbert space, the existence of the sixth solution is provided. Reviewer: Leszek Gasiński (Kraków) Cited in 2 Documents MSC: 35J66 Nonlinear boundary value problems for nonlinear elliptic equations Keywords:nodal solutions; nonlinear regularity; local minimizer; extremal solution; critical groups; superlinear reaction; concave term PDFBibTeX XMLCite \textit{S. Aizicovici} et al., Methods Appl. Anal. 22, No. 2, 221--248 (2015; Zbl 1322.35036) Full Text: DOI