Multiple and sign‐changing solutions for the multivalued p ‐Laplacian equation
Multiple and sign‐changing solutions for the multivalued p ‐Laplacian equation
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DOI：
10.1002/mana.200710049
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发表时间：
2010-07
影响因子：
1
通讯作者：
S. Carl;D. Motreanu
中科院分区：
文献类型：
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作者：
S. Carl;D. Motreanu
本文考虑一类Dirichlet边界条件下的椭圆包含，其中包含Clarke广义梯度的多个函数.在第一特征值和p-拉普拉斯算子的Fučik谱给出的条件下，我们证明了正解、负解和变号解的存在性。我们的方法是基于非光滑泛函的变分方法（非光滑临界点理论，第二变形引理），和多值椭圆问题的比较原理。特别是，极值常数符号解的存在性在变号解的证明中起着关键作用（© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
We consider a class of elliptic inclusions under Dirichlet boundary conditions involving multifunctions of Clarke's generalized gradient. Under conditions given in terms of the first eigenvalue as well as the Fučik spectrum of the p ‐Laplacian we prove the existence of a positive, a negative and a sign‐changing solution. Our approach is based on variational methods for nonsmooth functionals (nonsmooth critical point theory, second deformation lemma), and comparison principles for multivalued elliptic problems. In particular, the existence of extremal constant‐sign solutions plays a key role in the proof of sign‐changing solutions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)