Sign Changing Solutions of Superlinear Schrödinger Equations
Sign Changing Solutions of Superlinear Schrödinger Equations
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DOI：
10.1081/pde-120028842
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发表时间：
2003-03
影响因子：
1.9
通讯作者：
T. Bartsch;Zhaoli Liu;T. Weth
中科院分区：
文献类型：
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作者：
T. Bartsch;Zhaoli Liu;T. Weth
本文证明了具有超线性和次临界非线性项f的定常Schr dinger方程-Δu + a（x）u = f（x，u）在H1（N）中变号解的存在性，并控制了节点区域的个数。当f为奇数时，我们得到一个无界的变号解序列uk，k ≥ 1，使得uk至多有k + 1个节点域.结域的数量上的限制如下从一个非线性版本的柯朗的结域定理，我们也证明。
Abstract We prove the existence of sign changing solutions in H 1(ℝ N ) for a stationary Schrödinger equation −Δu + a(x)u = f(x, u) with superlinear and subcritical nonlinearity f, and control the number of nodal domains. If f is odd we obtain an unbounded sequence of sign changing solutions u k , k ≥ 1, so that u k has at most k + 1 nodal domains. The bound on the number of nodal domains follows from a nonlinear version of Courant's nodal domain theorem which we also prove.