This monograph presents fundamental methods and topics in nonlinear analysis and their
efficient application to nonlinear boundary value problems for elliptic equations. The book is …

In this paper we consider quasilinear elliptic equations with double phase phenomena and
a reaction term depending on the gradient. Under quite general assumptions on the …

In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined
effects of nonlinear singular and convection terms. An existence theorem for positive …

We study a nonlinear p (x)-Kirchhoff type problem with Dirichlet boundary condition, in the
case of a reaction term depending also on the gradient (convection). Using a topological …

In the present paper we prove a multiplicity theorem for a quasi-linear elliptic problem with
dependence on the gradient ensuring the existence of a positive solution and of a negative …

In this paper we study anisotropic weighted (p, q)-equations with a parametric right-hand
side depending on the gradient of the solution. Under very general assumptions on the data …

This paper presents existence and non-existence results on a positive solution for
quasilinear elliptic equations of the form− Δ ru− μ Δ r⁎ u= λ mr (x)| u| r− 2 u in Ω with 1< r≠ …

We are concerned with positive maximal and minimal solutions for non-homogeneous
elliptic equations of the form− div (a (|∇ u| p)|∇ u| p− 2∇ u)= f (x, u,∇ u) in Ω, supplied with …

The first part of this paper deals with existence of solutions to the quasilinear elliptic problem
(P)− div a (x,∇ u)= f (x, u,∇ u) in Ω, a (x,∇ u)⋅ ν= g (x, u)− ζ| u| p− 2 u on∂ Ω, involving a …

The existence of positive solutions for nonlinear elliptic problems under Dirichlet boundary
condition is studied as well as the compactness and directness of the solution set. The main …