American Institute of Mathematical Sciences

2003, 2003(Special): 83-90. doi: 10.3934/proc.2003.2003.83

Nonlinear boundary value problems with multiple positive solutions

 1 Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, United States, United States

Received  September 2002 Published  April 2003

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.
Citation: John V. Baxley, Philip T. Carroll. Nonlinear boundary value problems with multiple positive solutions. Conference Publications, 2003, 2003 (Special) : 83-90. doi: 10.3934/proc.2003.2003.83
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