IJPAM: Volume 27, No. 2 (2006)

POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH PERIODIC
BOUNDARY VALUE CONDITIONS

Chuanzhi BaiDepartment of Mathematics, Huaiyin Teachers College, Huaian, Jiangsu, 223001, P.R. CHINA
Department of Mathematics
Huaiyin Teachers College
Huaian, Jiangsu, 223001, P.R. CHINA
and
Department of Mathematics
Nanjing University
Nanjing, 210093, P.R. CHINA
e-mail: [email protected]


Abstract.Criteria are established for existence of positive solutions to the second order periodic boundary value problem

\begin{displaymath}- u^{\prime \prime}(t) + p u^{\prime}(t) + p_1 u(t) = f(t, u),\quad t \in I = [0, T], \end{displaymath}


\begin{displaymath}u(0) = u(T), \quad u^{\prime}(0) = u^{\prime}(T), \end{displaymath}

where $p \in {\bf R}$ and $p_1 \geq 0$. The discussion is based on the fixed point index theory in cones.

Received: August 10, 2005

AMS Subject Classification: 34B18

Key Words and Phrases: periodic boundary value problem, positive solution, cone, fixed point index

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 27
Issue: 2