Existence and multiplicity results for Pucci’s operators involving nonlinearities with zeros
Existence and multiplicity results for Pucci’s operators involving nonlinearities with zeros
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DOI：
10.1007/s00526-011-0465-0
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发表时间：
2011-12
影响因子：
2.1
通讯作者：
S. Alarcón;Leonelo Iturriaga;A. Quaas
中科院分区：
文献类型：
--
作者：
S. Alarcón;Leonelo Iturriaga;A. Quaas
我们研究了光滑有界区域上的问题$$ \left\{\begin{array}{ll} {-\varepsilon^{2}\mathcal{M}^+_{\lambda,\Lambda}(D^{2}u) = f (x, u)} \quad\; {\rm in} \; \Omega,\\ {u = 0} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad {\rm on} \; \partial{\Omega}, \end{array} \right.$$ whereΩis，并证明了当ε为一个正零的非负连续函数时，该问题具有小值的非平凡解。多重性的结果是基于次理论和一个新的Liouville型定理的非负非线性的零。
We study the problem $$ \left\{\begin{array}{ll} {-\varepsilon^{2}\mathcal{M}^+_{\lambda,\Lambda}(D^{2}u) = f (x, u)} \quad\; {\rm in} \; \Omega,\\ {u = 0} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad {\rm on} \; \partial{\Omega}, \end{array} \right.$$whereΩis a smooth bounded domain inand show it possesses nontrivial solutions for small values ofεprovidedfis a nonnegative continuous function which has a positive zero. The multiplicity result is based on degree theory together with a new Liouville type theorem forinfor nonnegative nonlinearities with zeros.