On strongly quasilinear elliptic systems with weak monotonicity

In this paper, we prove existence results in the setting of Sobolev spaces for a strongly quasilinear elliptic system by means of Young measures and mild monotonicity assumptions.

Comparison estimates on the first eigenvalue of a quasilinear elliptic system

We study a system of quasilinear eigenvalue problems with Dirichlet boundary conditions on complete compact Riemannian manifolds. In particular, Cheng comparison estimates and the inequality of Faber–Krahn for the first eigenvalue of a {(p,q)}-Laplacian are recovered. Lastly, we reprove a Cheeger-type estimate for the p-Laplacian, {1<p<\infty}, from where a lower bound estimate in terms of Cheeger’s constant for the first eigenvalue of a {(p,q)}-Laplacian is built. As a corollary, the first eigenvalue converges to Cheeger’s constant as {p,q\to 1,1}.

On positive weak solutions for a class of weighted (p(.), q(.))−Laplacian systems

In this paper, we study the existence of positive weak solutions for a quasilinear elliptic system involving weighted (p(.), q(.))−Laplacian operators. The approach is based on sub-supersolutions method and on Schauder’s fixed point theorem.

The Numbers of Positive Solutions by the Lusternik-Schnirelmann Category for a Quasilinear Elliptic System Critical with Hardy Terms

In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains. By employing the technique introduced by Benci and Cerami (1991), we obtain at least cat(Ω)+1 distinct positive solutions.