Infinitely many solutions to Kirchhoff double phase problems with variable exponents

In this work we deal with elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a right-hand side that is just locally defined in terms of very mild assumptions. Based on an abstract critical point result of Kajikiya (2005) and recent a priori bounds for generalized double phase problems by the authors (Ho and Winkert, 2022), we prove the existence of a sequence of nontrivial solutions whose L & INFIN;-norms converge to zero. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, we study elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a locally defined right-hand side. By using an abstract critical point result and recent a priori bounds, we prove the existence of a sequence of nontrivial solutions whose L∞-norms converge to zero.