Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1200.34025
Webb, J.R.L.; Infante, Gennaro
Semi-positone nonlocal boundary value problems of arbitrary order. (English)
[J] Commun. Pure Appl. Anal. 9, No. 2, 563-581 (2010). ISSN 1534-0392; ISSN 1553-5258/e

The authors develop a new unifying theory, which allows to study the existence of multiple positive solutions for semi-positone problems for differential equations of arbitrary order with a mixture of local and nonlocal boundary conditions. The nonlocal boundary conditions are quite general, they involve positive linear functionals on the space $C[0,1]$, given by Stieltjes integrals. These general BVPs are studied via a Hammerstein integral equation of the form $$ u(t)=\int_0^1 k(t,s)g(s) f(s,u(s))ds,$$ where $k$ is the corresponding Green's function which is supposed to have certain positivity properties, and $f:[0,1]\times [0,\infty)\to\Bbb R$ satisfies $f(t,u)\ge -A$ for some $A>0$. The proofs are based on fixed point index results. Examples of a second order and a fourth order problem are presented. Here, the authors determine explicit values of constants that appear in the theory.
[Irena Rach\uu nková (Olomouc)]

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
34B10 Multipoint boundary value problems
47H11 Degree theory
47H30 Particular nonlinear operators

Keywords: nonlocal boundary conditions; semi-positone; positive solution

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]