Abstract This paper concerns semilinear elliptic equations involving sign-changing weight function and a nonlinearity of subcritical nature understood in generalized sense. Using an Orlicz–Sobolev space setting, we consider superlinear nonlinearities which do not have polynomial growth, state sufficient conditions guaranteeing the Palais–Smale condition. We study existence bifurcated branch cla...

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...