Stationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain

In this work, we are mainly concerned with the existence of stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in $\mathbb{R}^n$ $$\left\{\begin{aligned} &\frac{\partial^3}{\partial x^3}u(x,y)+\frac{\partial}{\partial x}f(u(x,y))=D_x^{-1}\Delta_yu(x,y),\ \text{in}\ \Omega,\\ &D_x^{-1}u|_{\partial\Omega}=0,\ u|_{\partial\Omega}=0, \end{aligned}\right.$$ where $\Omega\in \mathbb{R}^n$ is a bounded domain with smooth boundary $\partial\Omega$. We utilize critical point theory to establish our main results

Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Damped Vibration Problems with Impulsive Effects

This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects. Some new results are obtained under more relaxed conditions by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory. The results obtained in this paper generalize and improve some existing works in the literature

Variational Approach to Impulsive Problems: A Survey of Recent Results

We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions