Existence of Multiple Solutions for Second Order Boundary Value Problems

Abstract

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y"+ f (x, y, y$)=0, x # [0, 1], y(0)=0= y(1). In the special case f (x, y, y$)= f ( y) 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al. 2000Academic Press

Infinitely Many Solutions for a Perturbed Quasilinear Two-Point Boundary Value Problem

“…For other basic notations and definitions, and for a thorough account on the subject, we refer the reader to [1,2,5,12,16,17,20,22,23,24,26,32].…”

The boundary value problems of quadratic mixed type of delay differential equations with eigenvalues

“…In the past years, the research work upon delay differential equations becomes more and more popular [3,[5][6][7][11][12][13]15,[17][18][19], because this kind of differential equations also have broad applied backgrounds in the fields of physics, biology and control principle [1,4]. The relative differential equations include two kinds, ie, differential equations with eigenvalues (see [3,7,14,18]) or without eigenvalues [13,13,15].…”

Multiple symmetric positive solutions for a second order boundary value problem

“…Other attention has been given to triple solutions in the paper by Anderson [1] for three-point boundary value problems for third order equations, as well as in the paper by Henderson and Thompson [5] for certain two-point boundary value problems for n-th order equations. Each of the papers [1], [2] and [5] makes an application of a fixed point theorem by Leggett-Williams [6], which they developed using the fixed point index in order Banach spaces.…”

“…Each of the papers [1], [2] and [5] makes an application of a fixed point theorem by Leggett-Williams [6], which they developed using the fixed point index in order Banach spaces. Leggett-Williams [6] applied their fixed point theorem to prove the existence of three positive solutions for Hammerstein integral…”