论文标题
非线性Helmholtz方程的双变异方法具有签名非线性
Dual variational methods for a nonlinear Helmholtz equation with sign-changing nonlinearity
论文作者
论文摘要
我们证明了非线性helmholtz方程的新生存结果，并改变形式的签名非线性 $$ - ΔU -k^{2} u = q（x）| u |^{p -2} u，\ quad u \ in w^{2，p}（\ mathbb {r}^{n}^{n}）$ \ left [\ left。由于$ Q $的签名变换，我们的解决方案在相应的双重变异配方中具有无限的摩尔斯山地指数。
We prove new existence results for a Nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$ - Δu - k^{2}u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}(\mathbb{R}^{N}) $$ with $k>0,$ $N \geq 3$, $p \in \left[\left.\frac{2(N+1)}{N-1},\frac{2N}{N-2}\right)\right.$ and $Q \in L^{\infty}(\mathbb{R}^{N})$. Due to the sign-changes of $Q$, our solutions have infinite Morse-Index in the corresponding dual variational formulation.
