Positive solutions of singular sublinear fourth-order boundary value problems

Abstract

We give some necessary and sufficient conditions for the existence of C 2 ½0, 1 and C 3 ½0, 1 positive solutions to the singular boundary value problem y 0000 ðtÞ ¼ pðtÞy ðtÞ, t 2 ð0, 1Þ,where: 2 ð0, 1Þ is given; and p : ð0, 1Þ ! ½0, 1Þ can be singular at both ends t ¼ 0 and t ¼ 1. We also give a sufficient condition for the existence of C 1 ½0, 1 positive solutions to the above problem. The proofs are based upon the method of lower and upper solutions for singular fourth-order boundary value problems.

Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

“…subject to different types of boundary conditions have been extensively studied (see, for example, [1][2][3][4][5][6][7][8][9][10][11] and the references therein). Under adequate conditions imposed on f and using different approach, the existence, uniqueness and qualitative properties of solutions have been considered.…”