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.


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