Existence of solutions for the one-phase and the multi-layer free-boundary problems with the -Laplacian operator.
Existence of solutions for the -Laplacian problem with singular term.
Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains.
Existence of weak solutions for elliptic Dirichlet problems with variable exponent
This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type where is a bounded domain of , . In particular, we do not require strict monotonicity of the principal part , while the approach is based on the variational method and results of the variable exponent function spaces.
Existence results for a class of semilinear degenerate elliptic equations
We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.
Existence results for quasilinear degenerated equations via strong convergence of truncations.
In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x,u,∇u) = f, where A is a Leray-Lions operator from W01,p(Ω,ω) into its dual, while g(x,s,ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s. The right hand side f is assumed to belong either to W-1,p'(Ω,ω*) or to L1(Ω).
Existence results for quasilinear elliptic systems in .
Existence results for singular anisotropic elliptic boundary-value problems.
Existence theorems for elliptic hemivariational inequalities involving the -Laplacian.
Extremal length of vector measures.