Existence and multiplicity of positive solutions for singular $\phi$-Laplacian superlinear problems with nonlinear boundary conditions

Abstract

We prove the existence and multiplicity of positive solutions to the singular phi-Laplacian BVP {-r(t)phi(u'))' = lambda g(t) (f(u) - a/u(alpha)), t is an element of(0,1), u(0) = 0, u'(1) + H(U(1)) = 0 for a certain range of the parameter lambda > 0, where a > 0, alpha is an element of (0,1), phi is an odd, increasing and convex homeomorphism on R, and f is phi-superlinear at infinity.