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Existence of positive radial solutions for a nonlinear elliptic problem in annulus domains

机译:环域上非线性椭圆问题正径向解的存在性。

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摘要

In this paper, we study a nonlinear elliptic problem in an annulus domain. For which, the nonexistence of nontrivial solutions has been obtained by some authors in star-shaped domain. Although we note that it may admit non-trivial solutions if the domain is non-star shaped. With the use of a variational method, we establish the existence of positive radial solutions in an annulus domain. On the basis of this, we also extend this result to the periodic problem of the corresponding degenerate parabolic problem.
机译:在本文中,我们研究了环域中的非线性椭圆问题。为此,一些作者已经在星形域中获得了非平凡解的不存在。尽管我们注意到,如果域是非星形的,则它可能会接受非平凡的解。通过使用变分方法,我们在环域中建立了正径向解的存在。在此基础上,我们还将这个结果扩展到相应的退化抛物线问题的周期问题。

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