Special Session 95: Nonlinear analysis and elliptic boundary value problems

Singular Kirchhoff problems with unbalanced-growth operators
Patrick Winkert
University of Technology Berlin
Germany
Co-Author(s):    Umberto Guarnotta
Abstract:
In this talk, we present existence results for Kirchhoff problems with singular and super-linear reaction terms. The operator is given in a general form, possibly non-homogeneous and with unbalanced growth. Under general assumptions, we prove the existence of two solutions with different energy sign by using the fibering map and the Nehari manifold. Our hypotheses cover the double phase operator and the logarithmic double phase operator as special cases. This is a joint work with Umberto Guarnotta (Ancona).