We will study a class of Steklov-Neumann boundary value problems for some quasilinear elliptic equations. We obtain result ensuring the existence of solutions when resonance and nonresonance conditions occur. The result was obtained by using variational arguments.

We study here a class of quasilinear elliptic systems involving the p-Laplacian operator. Under some suitable assumptions on the nonlinearities, we show the existence result by using a fixed point theorem.

The paper is concerned with the solvability of variational inequalities that contain second-order quasilinear elliptic operators and convex functionals. Appropriate concepts of suband supersolutions (for inequalities) are introduced and existence of solutions and extremal solutions are discussed.

We use Karamata regular variation theory to study the exact asymptotic behavior of large solutions near the boundary to a class of quasilinear elliptic equations with convection terms ⎧⎨ ⎩ Δpu±|∇u|q(p−1) = b(x) f (u), x ∈Ω,

We consider the Dirichlet problem for the quasilinear elliptic system − div σ(x, u(x), Du(x)) = f on Ω u(x) = 0 on ∂Ω for a function u : Ω → Rm, where Ω is a bounded open domain in Rn. For arbitrary right hand side f ∈W−1,p (Ω) we prove existence of a weak solution under classical regularity, growth and coercivity conditions, but with only very mild monotonicity assumptions.

In this paper we consider the quasilinear elliptic system ∆pu = uv, ∆pv = uv in a smooth bounded domain Ω ⊂ R , with the boundary conditions u = v = +∞ on ∂Ω. The operator ∆p stands for the p-Laplacian defined by ∆pu = div(|∇u|p−2∇u), p > 1, and the exponents verify a, e > p − 1, b, c > 0 and (a − p + 1)(e − p + 1) ≥ bc. We analyze positive solutions in both components, providing necessary and ...

We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group H. The model case is the nondegenerate p-Laplacean operator

In this paper, we consider the existence of multiple nontrivial solutions for some fourth order quasilinear elliptic boundary value problems. The weak solutions are sought by using variational methods.

We study the uniqueness of weak solutions for quasilinear elliptic equations in divergence form. Some counterexamples are given to show that our uniqueness result cannot be improved in the general case.