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Nonlinear boundary value problems with multiple positive solutions

Pages: 83 - 90, Issue Special, July 2003

 Abstract        Full Text (185.7K)              

John V. Baxley - Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, United States (email)
Philip T. Carroll - Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, United States (email)

Abstract: We give conditions on $f(y)$ which guarantee that the boundary value problem $T_ny(x) = f(y(x))$, 0 < $x$ < $A$, $y^(2j)$(0) = 0 = $y^(2j+1)(A)$, $j$ = 0, 1,... , $n$-1, where $T_n$ is the $n$th iterate of the operator $Ty(x)$ = -$(1)/( w(x))$ $(p(x)y'(x))'$, have a prescribed number of multiple positive solutions. Our main tool is a fixed point theorem of Krasnosel’skiĭ.

Keywords:  boundary value problems, multiple solutions, fixed points.
Mathematics Subject Classification:  Primary: 34B15.

Received: September 2002; Published: April 2003.