Triple positive solutions for the one-dimensional $p$-laplacian

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Zhanbing Bai
Mingfu Ma
Xiangqian Liang

Abstract

We consider the boundary value problem: $ \left(\varphi_p(x'(t))\right)'+ q(t)f(t, x(t), x'(t))=0, p>1, t \in [0, 1] $, with $ x(0)=x(1)=0 $, or $ x(0)=x'(1)=0 $. Using a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is the nonlinear term $ f $ is involved with the first order derivative. An example is also included to illustrate the importance of the results obtained

Article Details

How to Cite
Bai, Z., Ma, M., & Liang, X. (2006). Triple positive solutions for the one-dimensional $p$-laplacian. Tamkang Journal of Mathematics, 37(1), 15–25. https://doi.org/10.5556/j.tkjm.37.2006.176
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Papers
Author Biographies

Zhanbing Bai

College of Information Science & Technology, Shandong University of Science and Technology, Qingdao 266510, People’s Republic of China.

Mingfu Ma

Department of Applied Mathematics, University of Petroleum, Dongying 257061, People’s Republic of China.

Xiangqian Liang

College of Information Science & Technology, Shandong University of Science and Technology, Qingdao 266510, People’s Republic of China.