Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities (Q2516213)

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.