Izvorni znanstveni članak
Positive solutions for the system of higher order singular nonlinear boundary value problems
Kapula Rajendra Prasad
; Department of Applied Mathematics, Andhra University, Visakhapatnam, India
Allaka Kameswararao
; Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Madhurawada, Visakhapatnam, India
Sažetak
In this paper, by using Krasnosel'skii fixed point theorem and under suitable conditions, we present the existence of single and multiple positive solutions to the following systems
$$
\begin{aligned}
(-1)^mu^{(2m)}&=\lambda f(t, u(t), v(t))=0,~~~~ t\in[a, b],\\
(-1)^nv^{(2n)}&=\mu g(t, u(t), v(t))=0,~~~~ t\in[a, b],\\
u^{(2i)}(a)&=u^{(2i)}(b)=0,~~~~0\leq i\leq m-1,\\
v^{(2j)}(a)&=v^{(2j)}(b)=0,~~~~0\leq j\leq n-1,
\end{aligned}
$$
where $\lambda, \mu>0, m,n\in \N$. We derive two explicit eigenvalue intervals of $\lambda$ and $\mu$ for the existence of at least one
positive solution and the existence of at least two positive solutions for the above higher order two-point boundary value problem.
Ključne riječi
positive solutions; nonlinear ordinary di erential systems; singular boundary value problems; xed point theorem
Hrčak ID:
101383
URI
Datum izdavanja:
10.5.2013.
Posjeta: 1.278 *