EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N)
EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N)
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DOI：
10.1080/03605309508821149
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发表时间：
1995-01-01
影响因子：
1.9
通讯作者：
WANG, ZQ
中科院分区：
文献类型：
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作者：
BARTSCH, T;WANG, ZQ
研究了R(N)中的半线性椭圆偏微分方程u + b(x)u = f（x, u）。非线性f将是超线性和亚临界的。我们证明了b在各种假设下的正解的存在性。如果b(x) = α (x)+1且f在u中为奇数，那么我们还讨论了解的个数（可能是改变符号的）与参数λ的依赖关系。我们不假设b或f在x无穷时有极限。
We study the semilinear elliptic PDE -Delta u + b(x)u = f(x, u) in R(N). The nonlinearity f will be superlinear and subcritical. We prove the existence of a positive solution under various hypotheses on b. If b(x) = lambda alpha(x)+1 and f is odd in u, then we also discuss the dependence of the number of (possibly sign changing) solutions on the parameter lambda. We do not assume that b or f have a limit for \x\ --> infinity.