The method of lower and upper solutions for fourth order singular m-point boundary value problems |
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| Authors: | Zhongli Wei Changci Pang |
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| Institution: | Department of Mathematics and Physics, Shandong Institute of Architectural and Engineering, Jinan, Shandong 250014, People's Republic of China School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, People's Republic of China |
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| Abstract: | This paper investigates the existence of positive solutions for fourth order singular m-point boundary value problems. Firstly, we establish a comparison theorem, then we define a partial ordering in C20,1]∩C4(0,1) and construct lower and upper solutions to give a necessary and sufficient condition for the existence of C20,1] as well as C30,1] positive solutions. Our nonlinearity f(t,x,y) may be singular at x, y, t=0 and/or t=1. |
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| Keywords: | Singular m-point boundary value problem Positive solution Lower and upper solution Partial ordering Comparison theorem |
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