EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

doi:10.1016/S0252-9602(11)60228-2

Abstract

Abstract:

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equa-tions, and provide sufficient conditions for the existence and uniqueness of positive solu-tion to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.

Key words: Mixed monotone operator, fixed point theorem, boundary value problems, existence, uniqueness

CLC Number:

34B15

YUAN Cheng-Jun, WEN Xiang-Dan, JIANG Da-Qing. EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS[J].Acta mathematica scientia,Series B, 2011, 31(1): 281-291.

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