Positive solutions of nonlinear singular third-order two-point boundary value problem

Abstract

In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problemwhere λ is a positive parameter. Under various assumptions on a and f we establish intervals of the parameter λ which yield the existence of at least one, at least two, and infinitely many positive solutions of the boundary value problem by using Krasnoselskii's fixed point theorem of cone expansion-compression type.

On The Existence Of Multiple Solutions Of A Class Of Second-order Nonlinear Two-point Boundary Value Problems

“…The second factor motivating our work is the lack of theoretical framework capable of obtaining solutions. The great numbers of methods which involve upper and lower solutions being based on fixed-point theory [26][27][28][29][30][31][32][33][34][35][36][37] illustrate only the existence of some classes of solution without providing a real procedure to obtain them. Of course this is difficult task and sometimes impossible, however the present paper gives a proof, which is constructive in nature, for existence of multiple solutions of the problems (1)- (2) and (3)- (4), and obtain all branches of solutions (if they exist) at the same time.…”

Existence and Iteration of Positive Solutions to Third-Order BVP for a Class ofp-Laplacian Dynamic Equations on Time Scales

“…On the one hand, higher-order nonlinear boundary value problems have been studied extensively; for details, see [4,10,17,18] and references therein. On the other hand, the boundary value problems with -Laplacian operator have also been discussed extensively in the literature; for example, see [3, 7-9, 11, 19-21].…”

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

“…The current analysis of these problems has a great interest and many methods are used to solve such problems. Recently certain three point boundary value problems for nonlinear ordinary differential equations have been studied by many authors [1][2][3][4][5][6][7][8][9]. The literature concerning these problems is extensive and application of theorems of functional analysis has attracted more interest.…”

“…The literature concerning these problems is extensive and application of theorems of functional analysis has attracted more interest. Recently, the study of existence of positive solution to third-order boundary value problems has gained much attention and is a rapidly growing field see [1,2,6,[8][9][10][11]. However the approaches used in the literature are usually topological degree theory and fixed-point theorems in cone.…”