论文标题
非均匀的准线性椭圆问题：线性和sublerear案例
Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases
论文作者
论文摘要
我们关注的是由C.A.引入的非均匀差分运算符驱动的一类准线性椭圆方程。 Stuart且其研究是由非线性光学模型的动机。我们为至少有一个或两个非负解决方案建立了足够的条件。我们的分析考虑了反应具有肌关系或线性生长的情况。在Sublinear情况下，我们还证明了不存在的属性。这些证明结合了能量估计和变异方法。特别是，应用单调性技巧是为了克服宫殿序列上缺乏先验界限。
We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated by models in Nonlinear Optics. We establish sufficient conditions for the existence of at least one or two non-negative solutions. Our analysis considers the cases when the reaction has either a sublinear or a linear growth. In the sublinear case, we also prove a nonexistence property. The proofs combine energy estimates and variational methods. In particular, the monotonicity trick is applied in order to overcome the lack of a priori bounds on the Palais-Smale sequences.
