Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus
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摘要: 利用锥拉伸与锥压缩型的Krasnosel'skii不动点定理讨论了某些二阶非线性椭圆方程在环域上关于Dirichlet边界条件的正对径解的存在性。通过考察非线性项在有界闭区间上的性质建立了若干正对径解的存在性结论。主要结论不涉及非线性项的超线性增长和次线性增长。当非线性项存在极值并满足适当条件时,主要结论是非常有效的。Abstract: Applying Krasnoselc skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains,subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.
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Key words:
- second-order elliptic equation /
- annular domain /
- positve radial solution
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