Positive solutions for one-dimensional p-Laplacian boundary value problems with nonlinear parameter

Authors

  • Ahmed Omer Mohammed Abubaker Khartoum university, Faculty of Education, Sudan

DOI:

https://doi.org/10.14419/ijamr.v3i4.3168

Published:

2014-11-13

Abstract

In this paper, we establish existence of positive solutions of the nonlinear problems of one - dimensional p-Laplacian with nonlinear parameter\\

$ \varphi_p( u'(t))' +a(t) f(\lambda, u)=0,  \quad \ \ \ \ t \in (0,1) , \ \ \ u(0)= u(1)= 0.$\\

 where  $a: \Omega\rightarrow\mathbb{R}$  is continuous and may change sign, $\lambda>0$ is a parameter, $f(\lambda,0)>0$ for all $\lambda>0$. By applying Leray-Schauder fixed point theorem we obtain the existence of positive solutions.

 Keywords : p-Laplacian, Positive solutions, Leray-Schauder fixed point theorem, nonlinear parameter.

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