We study the Nehari manifold for a class of quasilinear elliptic systems involving a pair of (p,q)-Laplacian operators and a parameter. We prove the existence of a nonnegative nonsemitrivial solution for the systems by discussing properties of the Nehari manifold, and so global bifurcation results are obtained. Thanks to Picone’s identity, we also prove a nonexistence result.

This paper concerns quasilinear elliptic equations of the form −div(|∇u|p−2∇u) = λa(x)u(x)|u|p−2(1− |u|γ) in R with p > 1 and a(x) changes sign. We discuss the question of existence and multiplicity of solutions when a(x) has some specific properties. AMS subject classification: 35J70, 35B32, 35B40.

We prove comparison results between continuous and dis-continuous viscosity sub-and super-solutions of the generalized Dirichlet problem for quasilinear elliptic and parabolic equations. The main consequence of these results is the uniqueness of continuous solutions of such problems, when they exist.

We consider a prototype of quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of suband supersolutions on the basis of which we then develop the sub-supersolution method for variationalhemivariational inequalities. Furthermore, we give a...

We prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in R, n > 1, where f is either negative or positive for small u > 0, possibly singular at u = 0, and growths subcritically for large u. Our proofs use only elementary arguments based on a variational identity. No differentiability assumptions are made on f .

We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators Lpu := −∇ ∗ L(|∇Lu| ∇Lu). If φ is a positive weight such that −Lpφ ≥ 0, then the Hardy type inequality c ∫ Ω |u| φp |∇Lφ| p dξ ≤ ∫

In this paper, a class of quasilinear elliptic equations on the Heisenberg Group is concerned. Under some suitable assumptions, by virtue of the nonsmooth critical point theory, the existence of infinitely many weak solutions of the problems is obtained. Mathematics Subject Classification: 35J20, 35J25, 65J67

We establish an existence result for a class of quasilinear elliptic boundary value problems with jumping nonlinearities using variational arguments. First we calculate certain homotopy groups of sublevel sets of the asymptotic part of the variational functional. Then we use these groups to show that the full functional admits a linking geometry and hence a minmax critical point.

We present some results on the existence of bounded positive solutions to a class of nonlinear second order ordinary diferential equations by using the Schauder-Tikhonov fixed point theorem. An application to the existence of bounded positive solutions to certain quasilinear elliptic equations in two-dimensional exterior domains is also given.

In this paper, we prove existence and regularity of positive solutions for singular quasilinear elliptic systems involving gradient terms. Our approach is based on comparison properties, a priori estimates Schauder’s fixed point theorem.