On the existence of solutions of -Laplacian -point boundary value problem at resonance
β Scribed by Yanling Zhu; Kai Wang
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 433 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
β¦ Synopsis
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 β₯ 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 ) are allowable to be bigger than 1.
π SIMILAR VOLUMES
In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian (Ο p (u )) + q(t) f (t, u(t), u (t)) = 0, t β (0, 1), subject to the boundary conditions: where Ο p (s) = |s| p-2 s, p > 1, ΞΎ i β (0, 1) with 0 < ΞΎ 1 < ΞΎ 2 < β’ β’ β’ < ΞΎ m-2 < 1 and a i β [0, 1), 0 β€
Sufficient conditions for the existence of positive solutions of the nonlinear m-Laplacian boundary value problem are constructed, where m > 2 and f : [0, 1) x (0, oo) --\* (0, oo) satisfying f(t, u) is locally Lipschitz continuous for u 6 (0, cx)), and f(t,u)/u m-1 is strictly decreasing in u > 0