Infinitely Many Solutions for a Superlinear Fractional p -Kirchhoff-Type Problem without the (AR)‎ Condition

Abstract EN

In this paper, we investigate the existence of infinitely many solutions to a fractional p -Kirchhoff-type problem satisfying superlinearity with homogeneous Dirichlet boundary conditions as follows: [ a + b ( ∫ R 2 N u x - u y p K x - y d x d y ) ] L p s u - λ | u | p - 2 u = g x , u , i n Ω , u = 0 , i n R N ∖ Ω , where L p s is a nonlocal integrodifferential operator with a singular kernel K .

We only consider the non-Ambrosetti-Rabinowitz condition to prove our results by using the symmetric mountain pass theorem.