The existence of positive weak solutions to a singular quasilinear elliptic system in the whole space is established via suitable a priori estimates and Schauder's fixed point theorem.2010 Mathematics Subject Classification. 35J75; 35J48; 35J92.

This paper deals with boundedness results for weak solutions of the equation

A homogeneous Dirichlet problem with (p, q)-Laplace differential operator and reaction given by a parametric p-convex term plus a q-concave one is investigated. A bifurcation-type result, describing changes in the set of positive solutions as the parameter λ > 0 varies, is proven. Since for every admissible λ the problem has a smallest positive solutionū λ , both monotonicity and continuity of the map λ →ū λ are studied.2010 Mathematics Subject Classification. 35J20, 35J60.

In this paper we study double phase problems with nonlinear boundary condition and gradient dependence. Under quite general assumptions we prove existence results for such problems where the perturbations satisfy a suitable behavior in the origin and at infinity. Our proofs make use of variational tools, truncation techniques and comparison methods. The obtained solutions depend on the first eigenvalues of the Robin and Steklov eigenvalue problems for the p-Laplacian.

No abstract