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On the existence of m-point boundary value problem at resonance for higher order differential equation

โœ Scribed by Shiping Lu; Weigao Ge

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
225 KB
Volume
287
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

By means of Mawhin's continuation theorem, we study m-point boundary value problem at resonance in the following form:

x (k) (t) = f (t, x(t), x (t), . . . , x (k-1) (t)) + e(t), t โˆˆ (0, 1),

A new result on the existence of solutions is obtained. The interesting is that we do not need all the a i 's (1 i m -2) have the same sign, and also the degrees of some variables among x 0 , x 1 , . . . , x k-1 in the function f (t, x 0 , x 1 , . . . , x k-1 ) are allowable to be greater than 1. Meanwhile, we give some examples to demonstrate our result.

๐Ÿ“œ SIMILAR VOLUMES

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โœ Xiaojie Lin; Zengji Du; Weigao Ge ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 483 KB

This paper is concerned with the existence of solutions for the following nth-order multipoint boundary value problems at resonance case x(")(t)=r(t,~(t),~'(t) ..... :~(n-~) (t)) + e (t), te (0,1), m--2 (o) = ~' (o) ..... ~(,,-2) (o1 = o, ~ (i) = ~ ~j~ (,j), j=l and x (~) (t) = f (t,x (t),x' (t) ...

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โœ Yanling Zhu; Kai Wang ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 433 KB

By using the theory of coincidence degree, we study a kind of solutions of p-Laplacian m-point boundary value problem at resonance in the following form where m โ‰ฅ 3, a i > 0 A result on the existence of solutions is obtained. The degrees of two variables x 1 , x 2 in the function f (t, x 1 , x 2 )