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| Degenerate Nonlinear Elliptic Equations Lacking in Compactness |
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Citation： |
Maria MALIN,Cristian UDREA.Degenerate Nonlinear Elliptic Equations Lacking in Compactness[J].Chinese Annals of Mathematics B,2016,37(1):53~72 |
| Page view： 3401
Net amount： 1540 |
Authors： |
Maria MALIN; Cristian UDREA |
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| Abstract： |
In this paper, the authors prove the existence of solutions for
degenerate elliptic equations of the form
$-\mbox{div}(a(x)\nabla_{p}u(x))=g(\lambda,x,|u|^{p-2}u)$ in
$\mathbb{R}^N$, where $\nabla_{p}u=|\nabla u|^{p-2}\nabla u$ and
$a(x)$ is a degenerate nonnegative weight. The authors also
investigate a related nonlinear eigenvalue problem obtaining an
existence result which contains information about the location and
multiplicity of eigensolutions. The proofs of the main results are
obtained by using the critical point theory in Sobolev weighted
spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality and
by using a specific minimax method, but without making use of the
Palais-Smale condition. |
Keywords： |
Degenerate equations, $p$-Laplacian, Sobolev weighted spaces,
Mountain-pass theorem |
Classification： |
35J05, 35J50, 35J60, 35P30 |
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