On a class of Kirchhoff-Choquard equations involving variable-order fractional $p(\cdot)-$ Laplacian and without Ambrosetti-Rabinowitz type condition

TL;DR

This paper investigates the existence of solutions for a class of complex Kirchhoff-Choquard equations involving variable-order fractional p-Laplacian operators, without relying on the traditional Ambrosetti-Rabinowitz condition.

Contribution

It introduces new methods to establish solution existence for doubly nonlocal equations with variable-order fractional operators, bypassing the Ambrosetti-Rabinowitz condition.

Findings

Existence of weak solutions

Existence of ground state solutions

Multiple solutions via Fountain and Dual Fountain theorems

Abstract

In this article we study the existence of weak solution, existence of ground state solution using Nehari manifold and existence of infinitely many solutions using Fountain theorem and Dual fountain theorem for a class of doubly nonlocal Kirchhoff-Choquard type equations involving the variable-order fractional $p(\cdot)-$ Laplacian operator. Here the nonlinearity does not satisfy the well known Ambrosetti-Rabinowitz type condition.