Original scientific paper

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

Abstract

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.

Keywords

positive solutions; nonlinear ordinary dierential systems; singular boundary value problems; xed point theorem

Hrčak ID:

101383

URI

https://hrcak.srce.hr/101383

Publication date:

10.5.2013.

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