Existence of Positive Solutions of One-Dimensional Prescribed Mean Curvature Equation

Abstract EN

We consider the existence of positive solutions of one-dimensional prescribed mean curvature equation −(u′/1+u′2)′=λf(u), 00, t∈(0,1), u(0)=u(1)=0 where λ>0 is a parameter, and f:[0,∞)→[0,∞) is continuous.

Further, when f satisfies max{up,uq}≤f(u)≤up+uq, 0

The main results are based upon quadrature method.