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\$ φ_p( u'(t))' +a(t) f(λ, u)=0,Â t (0,1) , u(0)= u(1)= 0. Â whereÂ a: Ω→RÂ is continuous and may change sign, λ>0 is a parameter, f(λ,0)>0 for all λ>0. By applying Leray-Schauder fixed point theorem we obtain the existence of positive solutions.Â Keywords : p-Laplacian, Positive solutions, Leray-Schauder fixed point theorem, nonlinear parameter.