Open AccessOn fourth-order elliptic boundary value problems
Author(s) -
C. V. Pao
Publication year - 1999
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-99-05430-1
Subject(s) - uniqueness , mathematics , boundary value problem , monotone polygon , order (exchange) , mathematical analysis , class (philosophy) , value (mathematics) , function (biology) , nonlinear system , computer science , economics , geometry , physics , statistics , finance , quantum mechanics , artificial intelligence , evolutionary biology , biology
This paper is concerned with the existence and uniqueness of a solution for a class of fourth-order elliptic boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone nondecreasing or nonincreasing property of the nonlinear function. Sufficient conditions for the uniqueness of a solution and some techniques for the construction of upper and lower solutions are given. All the existence and uniqueness results are directly applicable to fourth-order two-point boundary value problems.