Atlas: Ambrosetti-Prodi type results for a higher order multi-pint boundary value problem by Lingju Kong

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6th International Conference on Differential Equations and Dynamical Systems
May 22-26, 2008

Baltimore, Maryland, USA

Organizers
Xinzhi Liu, University of Waterloo; Gaston M. N'Guerekata, Morgan State University

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Ambrosetti-Prodi type results for a higher order multi-pint boundary value problem
by
Lingju Kong
University of Tennessee at Chattanooga
Coauthors: John R. Graef (John-Graef@utc.edu) and Bo Yang (byang@kennesaw.edu)

We study the nth order multi-point boundary value problem

u⁽ⁿ⁾+f(t, u, u^', ..., u^(n-1))=lp(t), 0 < t < 1,

ì
ï
ï
í
ï
ï
î

u⁽ⁱ⁾(0)=A_i, i=0, ..., n-3,

u^(n-2)(0)- m
å
j=1
a_ju^(n-2)(t_j)=A_n-2,

u^(n-2)(1)- m
å
j=1
b_ju^(n-2)(t_j)=A_n-1.

Sufficient conditions are obtained for the existence of one and two solutions of the problem for different values of l. Our results extend and improve some recent work in the literature.

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Date received: January 11, 2008