Unbounded positive solutions for multi-point φ-Laplacian BVPs with sign-changing nonlinearities on the positive half-line

摘要

This work is concerned with the existence of positive solutions to a nonlinear multi-point boundary value problem posed on the positive half-line with a 0-Laplacian derivation operator. The nonlinearity depends on the solution and its derivative, may change sign, and has space singularities with respect to the solution and its derivative. It is also assumed to have quite general growth condi-tions. New existence results for nontrivial single and multiple positive solutions are proved using the fixed point index theory on cones of a weighted Banach space.