# Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative Dependence

Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative... The existence of multiple positive solutions is presented for the singular second-order boundary value problems $$\left\{\begin{array}{ll} x^{\prime\prime}+\Phi(t)f(t,x,x') =0, 0 < t < 1\\ x(0) = 0, x'(1) = 0 \end{array}\right.$$ using the fixed point index, where f may be singular at x  =  0 and x′  = 0. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative Dependence

, Volume 11 (4) – Sep 26, 2007
34 pages

/lp/springer_journal/multiple-positive-solutions-via-index-theory-for-singular-boundary-PlVcBQC7KS
Publisher
Birkhäuser-Verlag
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2068-8
Publisher site
See Article on Publisher Site

### Abstract

The existence of multiple positive solutions is presented for the singular second-order boundary value problems $$\left\{\begin{array}{ll} x^{\prime\prime}+\Phi(t)f(t,x,x') =0, 0 < t < 1\\ x(0) = 0, x'(1) = 0 \end{array}\right.$$ using the fixed point index, where f may be singular at x  =  0 and x′  = 0.

### Journal

PositivitySpringer Journals

Published: Sep 26, 2007

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