Nonlocal Kirchhoff Problems with Singular Exponential Nonlinearity

In this paper, we first develop the fractional Trudinger-Moser inequality in singular case and then we use it to study the existence and multiplicity of solutions for a class of perturbed fractional Kirchhoff type problems with singular exponential nonlinearity. Under some suitable assumptions, the existence of two nontrivial and nonnegative solutions is obtained by using the mountain pass theorem and Ekeland's variational principle as the nonlinear term satisfies critical or subcritical exponential growth conditions. Moreover, the existence of ground state solutions for the aforementioned problems without perturbation and without the Ambrosetti-Rabinowitz condition is investigated.

Automated summary

This paper first establishes the fractional Trudinger-Moser inequality in singular cases, and then uses it to study the existence and multiplicity of solutions for perturbed fractional Kirchhoff type problems with singular exponential nonlinearity. Under certain assumptions, the existence of two nontrivial and nonnegative solutions is obtained, and the existence of ground state solutions for the aforementioned problems without perturbation and without the Ambrosetti-Rabinowitz condition is also investigated.