POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS
Volume 2, Issue 2, pp 126-135
Publication Date: May 15, 2009
Authors
RAHMAT ALI KHAN
- Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
NASEER AHMAD ASIF
- Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
Abstract
Existence of positive solution for a class of singular boundary value
problems of the type
\[−x''(t) = f(t, x(t), x'(t)),\quad t \in (0, 1)\]
\[x(0) = 0, x(1) = 0,\]
is established. The nonlinearity \(f \in C((0, 1) \times (0,\infty) \times (−\infty,\infty), (−\infty,\infty))\)
is allowed to change sign and is singular at \(t = 0, t = 1\) and/or \(x = 0\). An
example is included to show the applicability of our result.
Keywords
- Positive solutions
- Singular differential equations
- Dirichlet boundary conditions.
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