On double phase Kirchhoff problems with singular nonlinearity

Abstract

In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcritical growth. Under very general assumptions on the data, we prove the existence of at least two weak solutions that have different energy sign. Our treatment is based on the fibering method in form of the Nehari manifold. We point out that we cover both the nondegenerate as well as the degenerate Kirchhoff case in our setting.

On a double phase problem of Kirchhoff-type with variable exponent

“…The same problem was studied in [17] by Fiscella and Pinamonti when p and q are constant, where the authors got a nontrivial solution via the critical point theory. Others recent results for constant case about this topic can be found in [3,16]. The sub-supersolution approach is a power tool to study the existence and multiplicity of solutions for nonlinear problems.…”