Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation

Abstract In this paper, we study the following generalized Kadomtsev-Petviashvili equation u t + x ( h ) = D − 1 Δ y , {u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where xmlns:m="http://www.w3.org/1998/Math/MathML"> ∈ mathvariant="double-struck">R × N \left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R}}\times {{\mathbb{R}}}^{N-1} , ≥ 2 N\ge 2 f ∫ ∞ s mathvariant="normal">d {D}_{x}^{-1}f\left(x,y)={\int }_{-\infty }^{x}f\left(s,y){\rm{d}}s ∂ {f}_{t}=\frac{\partial f}{\partial t} {f}_{x}=\frac{\partial x} and ∑ i {\Delta }_{y}={\sum }_{i=1}^{N-1}\frac{{\partial }^{2}}{{\partial }_{{y}_{i}}^{2}} . We get existence of infinitely many nontrivial solutions under certain assumptions in bounded domain without Ambrosetti-Rabinowitz condition. Moreover, by using method developed Jeanjean [13], establish ground state {{\mathbb{R}}}^{N}