Unbounded positive solutions for multi-point $\phi$-Laplacian bvps

Abstract

This work is concerned with the existence of positive solutions for a nonlinear multi-point boundary value problem posed on the positive half-line with a $\phi$-Laplacian derivation operator. The nonlinearity depends on the solution and its derivative, may change sign and have space singularities with respect to the solution and its derivative. It is also assumed to have quite general growth conditions. New existence results of nontrivial single and multiple positive solutions are proved using the index fixed point theory on cones of a weighted Banach space.