IJPAM: Volume 61, No. 1 (2010)

EIGENVALUE INTERVALS FOR $3n$-TH ORDER
THREE-POINT BOUNDARY VALUE PROBLEMS

K.R. Prasad$^1$, K.L. Saraswathi Devi$^2$
$^{1,2}$Department of Applied Mathematics
Andhra University
Visakhapatnam, 530 003, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^2$Department of Mathematics
Ch.S.D. St. Theresa's Degree College for Women
Eluru, 534 003, INDIA


Abstract.We study the existence of eigenvalue intervals of $\lambda$, for which there exist a positive solution with respect to a cone, of the $3n$-th order three-point boundary value problem

\begin{displaymath}{(-1)}^ny^{(3n)}=\lambda f(t,y(t)),~~~t\in[t_1,t_3],\end{displaymath}

subject to general three-point boundary conditions

\begin{displaymath} \begin{aligned} \alpha_{3i-2,1}y^{(3i-3)}(t_1)+\alpha_{3i-2,... ...}y^{(3i-2)}(t_3)+\alpha_{3i,3}y^{(3i-1)}(t_3)&=0, \end{aligned}\end{displaymath}

for $1\leq i\leq n,$ where $n\geq1$, $t_1<t_2<t_3$ and $f:[t_1,t_3]\times \R\rightarrow \R$ is continuous, $\lambda$ is a parameter.

Received: April 24, 2010

AMS Subject Classification: 34B15, 39B18, 39A10

Key Words and Phrases: boundary value problem, eigenvalue interval, positive solution, cone

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 1