Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1005.47051
Avery, R.I.; Peterson, A.C.
Three positive fixed points of nonlinear operators on ordered Banach spaces. (English)
[J] Comput. Math. Appl. 42, No.3-5, 313-322 (2001). ISSN 0898-1221

The authors generalize the triple fixed-point theorem of Leggett and Williams, which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a Banach space. As an application of the abstract result, the authors prove the existence of three positive symmetric solutions of the discrete second-order nonlinear conjugate boundary value problem $$\Delta^2 x(t-1)+f(x(t))=0, \text{for all} t\in [a+1,b+1],$$ $$x(a)=0=x(b+2),$$ where $f: \Bbb R\to \Bbb R$ is continuous and $f$ is nonnegative for $x\ge 0.$
[S.K.Ntouyas (Ioannina)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
34B15 Nonlinear boundary value problems of ODE
39A05 General theory of difference equations
47N20 Appl. of operator theory to differential and integral equations
65J15 Equations with nonlinear operators (numerical methods)
65Q05 Numerical methods for functional equations

Keywords: fixed point theorems; difference equations; positive solutions; boundary; positive symmetric solutions; discrete second-order nonlinear conjugate boundary value problem

Cited in: Zbl 1235.34179 Zbl 1253.34057 Zbl 1249.34082 Zbl 1244.34041 Zbl 1240.34143 Zbl 1209.34077 Zbl 1197.34039 Zbl 1192.34072 Zbl 1182.34041 Zbl 1177.34031 Zbl 1170.34046 Zbl 1157.34015 Zbl 1181.39001 Zbl 1164.34369 Zbl 1153.34009 Zbl 1137.39007 Zbl 1135.34012 Zbl 1120.39019 Zbl 1115.34017 Zbl 1085.34011 Zbl 1069.34090 Zbl 1067.34020 Zbl 1055.34046 Zbl 1047.34075

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]