论文标题
超线性klein-gordon-Maxwell方程的多个解决方案
Multiple solutions for superlinear Klein-Gordon-Maxwell equations
论文作者
论文摘要
在本文中，我们考虑以下klein-gordon-maxwell方程\ begin {eqnarray*} \ left \ {\ oken {array} {ll} {ll}-ΔU+v（x） -uΔdation+ ϕu^2 =-ΩU^2＆\ mbox {in $ \ Mathbb {r}^{3} $}，\ end {array} \ right。 \ end {eqnarray*}其中$ω> 0 $是常数，$ u $，$ ϕ：\ MATHBB {r}^{3} {3} \ rightarrow \ Mathbb {r} $，$ v：\ Mathbb {r}通过假设$ v $的强制性条件以及$ f $上的一些新的超级线性条件，当$ h $不是零时，当$ f $在$ u $中是奇数和上述方程式中的$ h \ equiv0 $时，我们将获得两种非平凡解决方案。
In this paper, we consider the following Klein-Gordon-Maxwell equations \begin{eqnarray*} \left\{ \begin{array}{ll} -Δu+ V(x)u-(2ω+ϕ)ϕu=f(x,u)+h(x)&\mbox{in $\mathbb{R}^{3}$},\\ -Δϕ+ ϕu^2=-ωu^2&\mbox{in $\mathbb{R}^{3}$}, \end{array} \right. \end{eqnarray*} where $ω>0$ is a constant, $u$, $ϕ: \mathbb{R}^{3}\rightarrow \mathbb{R}$, $V : \mathbb{R}^{3} \rightarrow\mathbb{R}$ is a potential function. By assuming the coercive condition on $V$ and some new superlinear conditions on $f$, we obtain two nontrivial solutions when $h$ is nonzero and infinitely many solutions when $f$ is odd in $u$ and $h\equiv0$ for above equations.
