Positive solutions of an integral boundary value problem for singular differential equations of mixed type with \(p\)-Laplacian

Volume 9, Issue 12, pp 6048--6057 http://dx.doi.org/10.22436/jnsa.009.12.12

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Authors

Changlong Yu - College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China. Jufang Wang - College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China. Yanping Guo - College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.

Abstract

In this paper, by Leggett-William fixed point theorem, we establish the existence of triple positive solutions of a new kind of integral boundary value problem for the nonlinear singular differential equations with \(p\)-Laplacian operator, in which \(q(t)\) can be singular at \(t = 0; 1\). We also show that the results obtained can be applied to study certain higher order mixed boundary value problems. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.

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Keywords

• Positive solutions
• integral boundary value problem
• Leggett-William fixed point theorem
• p-Laplacian operator
• cone.

MSC

•  34B15
•  34B16
•  34B18
•  34G20

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