Positive solutions for one-dimensional p-Laplacian boundary value problems with nonlinear parameter - Abubaker, Ahmed Omer Mohammed (International Journal of Applied Mathematical Research, 2014)
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.