In this article, we study the existence of positive solutions for the quasilinear elliptic system −∆pu = f(x, u, v) x ∈ Ω, −∆pv = g(x, u, v) x ∈ Ω, u = v = 0 x ∈ ∂Ω. Using degree theoretic arguments based on the degree map for operators of type (S)+, under suitable assumptions on the nonlinearities, we prove the existence of positive weak solutions.

In this paper we find explicit lower bounds for Dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p-Laplace equation. Also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value.

We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the hp-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for the semidiscrete case for simplicity, allowing to focus on the challenges of a posteriori error control of IPDG space-discretizations of strictly monotone quas...

A class of quasilinear systems for geometric objects is studied near a point of elliptic degeneracy. 1991 MSC: 58E15, 81T13, 76N10.

We obtain necessary and sufficient conditions for the existence of positive solutions for a class of sublinear Dirichlet quasilinear elliptic systems.

In this paper, we study the regularity of solutions of the quasilinear equation where X = ( X , ; . . , X , , , ) is a system of real smooth vector fields, A i j , B E Cw(Q x R m + l ) . Assume that X satisfies the Hormander condition and ( A , , ( x , z , c ) ) is positive definite. We prove that if u E S2@(Q) (see Section 2) is a solution of the above equation, then u E Cw(Q). Introduction In...

We study the indefinite quasilinear elliptic problem −∆u−∆pu = a(x)|u|q−2u− b(x)|u|s−2u in Ω,

Elliptic equations model the behaviour of scalar quantities u, such as temperature or gravitational potential, which are in an equilibrium situation subject to certain imposed boundary conditions. In his first four lectures, John Urbas discussed linear 1 elliptic equations. In his lectures on the minimal surface equation, Graham Williams discussed the minimal surface equation, a quasilinear 2 e...

We show the existence of nodal solutions to perturbed quasilinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds. A nonexistence result is also given.