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In this paper, we study the following generalized Kadomtsev-Petviashvili equation ut+uxxx+(h(u))x=Dx−1Δyu,{u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where (t,x,y)∈R+×R×RN−1\left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R}}\times {{\mathbb{R}}}^{N-1}, N≥2N\ge 2, Dx−1f(x,y)=∫−∞xf(s,y)ds{D}_{x}^{-1}f\left(x,y)={\int }_{-\infty }^{x}f\left(s,y){\rm{d}}s, ft=∂f∂t{f}_{t}=\frac{\partial f}{\partial t}, fx=∂f∂x{f}_{x}=\frac{\partial f}{\partial x} and Δy=∑i=1N−1∂2∂yi2{\Delta }_{y}={\sum }_{i=1}^{N-1}\frac{{\partial }^{2}}{{\partial }_{{y}_{i}}^{2}}. We get the existence of infinitely many nontrivial solutions under certain assumptions in bounded domain without Ambrosetti-Rabinowitz condition. Moreover, by using the method developed by Jeanjean [13], we establish the existence of ground state solutions in RN{{\mathbb{R}}}^{N}.

In this paper, we study the following modified quasilinear Schrödinger equation − Δ u + V (x) u − κ u Δ (u 2) + q h 2 (| x |) | x | 2 (1 + κ u 2) u + q ∫ | x | + ∞ h (s) s (2 + κ u 2 (s)) u 2 (s) d s u = | u | p − 2 u i n R 2 , where κ > 0 , q>0, p>6 and V ∈ C ( R 2 , R). We develop a more direct and simpler approach to prove the existence of ground state solutions. Our method is based on the Poho z ˇ aev type identity and monotone trick. [ABSTRACT FROM AUTHOR]