Singular $\phi $-Laplacian third-order BVPs with derivative dependance

Abstract

This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a φ-Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition is assumed. An example of application illustrates the applicability of the existence result.

Positive solution for singular third-order BVPs on the half line with first-order derivative dependence

“…Naturally, in such boundary value problems, the nonlinearity may have a singular dependence on time or on the space variable. This was the case in the papers [3,6,7,8,20,21,27,28,29], which motivated this work.…”

“…Study of existence of positive solutions for third-order bvps has received a great deal of attention and was the subject of many articles, see, for instance, [10,11,12,13,14,21,25,27,28,29,30,31], for the case of finite intervals and [1,2,3,4,6,7,8,9,16,19,20,24,26] for the case posed on the halfline. Naturally, in such boundary value problems, the nonlinearity may have a singular dependence on time or on the space variable.…”