Existence of solutions for degenerate Kirchhoff type problems with fractional p-Laplacian

In this article, by using the Fountain theorem and Mountain pass theorem in critical point theory without Palais-Smale (PS) condition, we show the existence and multiplicity of solutions to the degenerate Kirchhoff type problem with the fractional p-Laplacian $$\displaylines{ \Big(a + b\int\int_{\mathbb{R}^{2N}} \frac{|u (x) - u (y)|^p}{|x - y|^{N + ps}} \, dx \, dy\Big) (- \Delta)_p^s u = f (x, u ) \quad \text{in } \Omega,\cr u = 0 \quad \text{in } \mathbb{R}^N \setminus \Omega, }$$ where $(- \Delta)_p^s$ is the fractional p-Laplace operator with $0 < s < 1 < p < \infty$, $\Omega$ is a smooth bounded domain of $\mathbb{R}^N$, N > 2 s, a, b > 0 are constants and $f: \Omega \times \mathbb{R} \to \mathbb{R}$ is a continuous function