Existence of positive solutions for the one-dimension singular \(P\)-laplacian equation with sign changing nonlinearities via the method of upper and lower solution. (English) Zbl 1079.34511

Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.

Methods Appl. Anal. 10, No. 4, 533-542 (2003).

Summary: A result concerning the existence of positive solutions for the Dirichlet boundary value problem \[ -(\varphi_p(u'))'=f(t,u),\;t\in (0,1),\;u(0)= c>0\text{ and }u(1)=0, \] is given in this paper. Here, \(f(t,y)\) may change sign and may be singular at \(y=0\).

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16	Singular nonlinear boundary value problems for ordinary differential equations