Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem
Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem
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发表时间：
2011-08
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通讯作者：
I. Ianni
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作者：
I. Ianni
考虑了$\R^3 $中的Schr\“odinger-Poisson-斯莱特（SPS）方程组和$\mathbb R^3$中的非局部SPS型方程，并讨论了Dirichlet边界条件.我们表明，对于每一个$k\在\mathbb N$每个问题考虑承认一个节点的径向对称的解决方案，改变了签署准确的径向变量$k$倍。当区域是$\mathbb R^3$的球时，我们得到了在任意时刻具有$k+1$个节点区域的非局部抛物问题的径向整体解的存在性.
We consider the Schr\"odinger-Poisson-Slater (SPS) system in $\R^3$ and a nonlocal SPS type equation in balls of $\mathbb R^3$ with Dirichlet boundary conditions. We show that for every $k\in\mathbb N$ each problem considered admits a nodal radially symmetric solution which changes sign exacly $k$ times in the radial variable. Moreover when the domain is the ball of $\mathbb R^3$ we obtain the existence of radial global solutions for the associated nonlocal parabolic problem having $k+1$ nodal regions at every time.