Special Session 90: NONLINEAR ELLIPTIC DIFFERENTIAL EQUATIONS AND APPLICATIONS

Nonlocal Carrier`s Double Phase Problem
Giuseppe Failla
University of Palermo
Italy
Co-Author(s):    Leszek Gasi\`nski
Abstract:
We investigate the existence and multiplicity of positive bounded solutions for a class of nonlocal, non-variational elliptic problems driven by a non-homogeneous operator with unbalanced growth, namely the double phase operator. The problem is characterized by the presence of a sign-changing weight function on the left-hand side. Our approach combines several techniques, including the sub- and super-solutions method, variational and truncation techniques, as well as tools from set-valued analysis. Furthermore, we analyze an associated one-dimensional fixed-point problem that allows us to prove the existence of $K>0$ pairs of positive solutions.