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On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded
Asymptotic Analysis ( IF 1.4 ) Pub Date : 2020-06-19 , DOI: 10.3233/asy-201626
Luca Esposito 1 , Prosenjit Roy 2 , Firoj Sk 2
Affiliation  

We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone identity to overcome nonlinearity complications. Altogether the use of Picone identity makes the proof easier with respect to the known proof in the linear case. Surprisingly the asymptotic behavior under mixed boundary conditions critically differs from the case of pure Dirichlet boundary conditions for some class of problems.

中文翻译:

关于无界域中非线性椭圆问题特征值的渐近行为

我们分析了在 Dirichlet 边界条件和混合(Dirichlet,Neumann)边界条件下非线性椭圆问题特征值的渐近行为,域变得无界。我们大量使用 Picone 标识来克服非线性复杂性。总之,相对于线性情况下的已知证明,使用 Picone 恒等式使证明更容易。令人惊讶的是,对于某些类别的问题,混合边界条件下的渐近行为与纯狄利克雷边界条件的情况截然不同。
更新日期:2020-06-19
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