## 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

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
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