Kirchhoff–Schrödinger-type problems involving double phase operator in Musielak–Orlicz–Sobolev spaces

Abstract

Abstract This work deals with a class of double phase problems with variable exponents of Kirchhoff–Schrödinger type within the framework of Musielak–Orlicz–Sobolev spaces. By imposing certain assumptions and using the topological degree for a class of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:msub> <m:mi>S</m:mi> <m:mo>+</m:mo> </m:msub> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(S_{+})} -demicontinuous operators, we derive the existence of at least one solution for the above problems. Our results are also applicable to problems with no-flux boundary conditions, and extend and generalize many previously published results.