Existence and uniqueness results for a third-order implicit differential equation

Authors:
Yuqiang Feng
Affiliations:
School of Science, Wuhan University of Science and Technology, Wuhan 430065, PR China and Department of Mathematics, Tsinghua University, Beijing, 100084, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

The purpose of this paper is to give sufficient conditions for the existence and uniqueness of solutions to the boundary value problem of a third-order implicit differential equation as follows: {f(t,u(t),u^'(t),u^@?(t))=0,0@?t@?1u(0)=u^'(0)=u^'(1)=0. The lower and upper solutions method, maximum principle together with an iterative technique are employed. An example illustrates the application of results obtained.