WEAK LINKING THEOREMS AND SCHR¨ ODINGER EQUATIONS WITH CRITICAL SOBOLEV EXPONENT
WEAK LINKING THEOREMS AND SCHR¨ ODINGER EQUATIONS WITH CRITICAL SOBOLEV EXPONENT
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DOI：
10.1051/cocv:2003029
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发表时间：
2003-08
期刊：
影响因子：
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通讯作者：
M. Schechter;W. Zou
中科院分区：
文献类型：
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作者：
M. Schechter;W. Zou
本文建立了一个变形的广义弱连接定理，它包含了更精细的结果，并保证了强单调泛函的有界Palais{Smale}序列的存在性.利用抽象结果研究了半线性Schrodinger方程u + V（x）u = K（x）juj 2 2 u +g（x;u）;u2 W 1;2（RN），其中N4;V;K;g是xj中的周期，对1 jN，0是在+V ; K> 0的谱间隙中.对适当的常数c，若0 <g（x;u）u cjuj 2，我们证明了该方程有非平凡解.
In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais{Smale sequences of a strongly indenite functional. The abstract result will be used to study the semilinear Schrodinger equation u + V (x)u = K(x)juj 2 2 u +g(x;u);u2 W 1;2 (R N ), where N 4;V;K;g are periodic inxj for 1 j N and 0 is in a gap of the spectrum of +V ; K> 0. If 0 <g (x;u)u cjuj 2 for an appropriate constant c, we show that this equation has a nontrivial solution.