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

作者：Wei, Li; Agarwal, Ravi P.; Wong, Patricia J. Y.^*

来源：Boundary Value Problems, 2016, 2016(1): 179.

DOI：10.1186/s13661-016-0683-7

• accretive mapping
• duality mapping
• subdifferential
• hyperbolic equation
• mixed boundaries

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.

• 出版日期2016-10-12
• 单位河北经贸大学