@article {142, title = {EXISTENCE OF POSITIVE SOLUTIONS TO A SYSTEM OF SINGULAR BOUNDARY VALUE PROBLEMS}, journal = {Dynamic Systems and Applications}, volume = {19}, year = {2010}, month = {2010}, pages = {10}, chapter = {395}, abstract = {

Existence results for positive solutions of a coupled system of nonlinear singular two point boundary value problems of the type

\  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  -x ''(t) = p( t ) f(t, y( t ),\ x' (t) ),\  \  \  \  \  \  \  \  \  \  t ∈ (0, 1),

\  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  -y ''(t) = q( t ) g(t, x( t ),\ y' (t) ),\  \  \  \  \  \  \  \  \  \ t ∈ (0, 1),

\  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  a1x(0) - b1x ' (0) = x ' (1) = 0,

\  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  \  a2y(0) - b2y ' (0) = y ' (1) = 0,

are established. The nonlinearities f, g : [0, 1] {\texttimes} [0, $\infty$) {\texttimes} (0, $\infty$) {\textrightarrow} [0, $\infty$) are allowed to be singular at x ' = 0 and y ' = 0. The functions p, q ∈ C(0, 1) are positive on (0, 1) and the constants ai , bi (i = 1, 2) \> 0. An example is included to show the applicability of our result.

}, keywords = {34B15, 34B16, 34b18}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/19/28-DSA-29-13.pdf}, author = {NASEER AHMAD ASIF and RAHMAT ALI KHAN and JOHNNY HENDERSON} }