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.
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.
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 quasilinear elliptic systems with nonlinear boundary condition with fully coupled perturbations even on the boundary. Under very general assumptions our main result says that each weak solution of such systems belongs to L ∞ (Ω) × L ∞ (Ω). The proof is based on Moser's iteration scheme. The results presented here can also be applied to elliptic systems with homogeneous Dirichlet boundary condition.2010 Mathematics Subject Classification. 35J57, 35J60, 35B45. Key words and phrases. Moser iteration, boundedness of solutions, a-priori bounds, elliptic operators of divergence type, elliptic systems, critical growth, coupled systems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.