New applications of Calvert and Gupta’s results to hyperbolic differential equation with mixed boundaries

Boundary value problems

Ravi P Agarwal²  Patricia JY Wong³  Li Wei⁴ 

[1] Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;Department of Mathematics, Texas A&M University - Kingsville, Kingsville, USA;School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, China

关键词: accretive mapping;    duality mapping;    subdifferential;    hyperbolic equation;    mixed boundaries;    47H05;    47H09;   

DOI  :  10.1186/s13661-016-0683-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Calvert and Gupta’s results concerning the perturbations on the ranges of m-accretive mappings have been employed widely in the discussion of the existence of solutions of nonlinear elliptic differential equation with Neumann boundary. In this paper, we shall focus our attention on certain hyperbolic differential equation with mixed boundaries. By defining some suitable nonlinear mappings, we shall demonstrate that Calvert and Gupta’s results can be applied to hyperbolic equations, in addition to its wide usage in elliptic equations. Due to the differences between hyperbolic and elliptic equations, some new techniques have been developed in this paper, which can be regarded as the complement and extension of the previous work.

【 授权许可】

CC BY