SINGULAR SEMI-POSITONE φ-LAPLACIAN BVP ON INFINITE INTERVAL IN BANACH SPACES

In this work, we have obtained new existence results of unbounded positive solutions for a second-order φ-Laplacian equation subject to nonlinear integral boundary conditions of Riemann-Stieltjes type and posed on the positive half-line. The index fixed point theory on cones of Banach spaces for countably strict set-contractions has been employed. The nonlinearity depends on the solution and its derivative, may change sign, and has time and space singularities in its arguments. It further takes values in a general Banach space and is assumed to have quite general growth conditions. We have illustrated our theoretical results with two examples of application in a finite and in an infinite dimensional space, respectively.