研究非线性Neumann 问题(p(t)u')'+q(t)u=f(t, u), t ∈ (0, 1), u'(0)=u'(1)=0,正解的存在性, 其中p, q ∈ C[0, 1]满足p > 0, 0 < q < b* in [0, 1], b*为线性问题(p(t)u')'+bu=0, u'(0)=0, u(1)=0的第一特征值. 运用拓扑度理论及Rabinowitz全局分歧定理为上述问题建立了正解的存在性结果.
Abstract
We are concerned with the existence of positive solutions of the nonlinear Neumann problem (p(t)u')'+q(t)u=f(t, u), t ∈ (0, 1), u'(0)=u'(1)=0, where p, q ∈ C[0, 1] with p > 0, 0 < q < b* in [0, 1], b* is the first eigenvalue of the Robin problem (p(t)u')'+bu=0, u'(0)=0, u(1)=0. By applying the topological degree theory and global bifurcation techniques, we establish the existence results of positive solutions for above problem.
关键词
存在性 /
特征值 /
Neumann问题 /
分歧方法 /
正解
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Key words
existence /
eigenvalues /
Neumann problem /
bifurcation methods /
positive solutions
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参考文献
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脚注
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基金
国家自然科学基金资助项目(11061030);国家自然科学天元基金资助项目(11226132);高校基本科研业务费专项资金资助项目(212084)
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