Zeitschrift für Analysis und ihre Anwendungen 22 (2003), No. 3, 689--709
Copyright Heldermann Verlag 2003
A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian
Ravi P. Agarwal
Dept. of Mathematics, Florida Inst. of Technology, Melbourne, FL 32901, U.S.A.
Haishen Lü
Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China
Donal O'Regan
Dept. of Mathematics, National University, Galway, Ireland
[Abstract-pdf]
This paper studies the boundary value problem $$ (\varphi_p(u'))' + q(t)(f(u) + g(u)) = 0 \qquad (0 < t < 1) $$ $$ \ \ u(0) = u(1) = 0 $$ in the case $p > 1$. A necessary and sufficient condition for the existence of $C^1[0,1]$ positive solutions and a sufficient condition for the existence of $C[0,1]$ positive solutions are presented.
Keywords: Singular boundary value problems, positive solutions, existence conditions for solutions.
MSC: 34B16; 39A10
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