POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS
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.
MSC
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