Anouar Bahrouni , Hlel Missaoui , Vicenţiu D. Rădulescu
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引用次数: 0
摘要
在本文中,我们考虑了一个由 Orlicz g-Laplacian 算子驱动的非线性 Robin 问题。利用变分技术结合适当的截断和莫尔斯理论(临界群),我们证明了所有解的两个带有符号信息的多重性定理。在第一个定理中,我们确定了至少存在两个具有固定符号的非微观解。在第二个定理中,我们证明了至少存在三个具有符号信息(一个正,一个负,另一个改变符号)和阶次的非微分解。对于具有 Robin 边界条件的非线性 g-Laplacian 问题来说,节点解的结果是新的。
Nodal solutions for the nonlinear Robin problem in Orlicz spaces
In this paper we consider a non-linear Robin problem driven by the Orlicz -Laplacian operator. Using variational technique combined with a suitable truncation and Morse theory (critical groups), we prove two multiplicity theorems with sign information for all the solutions. In the first theorem, we establish the existence of at least two non-trivial solutions with fixed sign. In the second, we prove the existence of at least three non-trivial solutions with sign information (one positive, one negative, and the other change sign) and order. The result of the nodal solution is new for the non-linear -Laplacian problems with the Robin boundary condition.
期刊介绍:
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.