Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave-convex nonlinearities

Abstract

In this paper, we are interested in the multiplicity of solutions for a non-homogeneous p-Kirchhoff-type problem driven by a non-local integro-differential operator. As a particular case, we deal with the following elliptic problem of Kirchhoff type with convex-concave nonlinearities: [a + b(∫ℝ2N |u(x) - u(y)|p/|x - y|N+sp dx dy)θ-1](-Δ)psu=λω1(x)|u|q-2u + ω2(x)|u|r-2u + h(x) inℝN, where (-Δ)ps is the fractional p-Laplace operator, a + b>0 with a, b ε ℝ0+, λ > 0 is a real parameter, 0 < s < 1 < p < ∞ with sp < N, 1 < q < p ≤ θp < r