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Exact number of positive solutions for a class of semipositone problems. (English) Zbl 1028.34027
The author considers the nonlinear eigenvalue problem \[ y''(t)= \lambda(y^p(t)- y^q(t)),\quad 0< t< 1,\qquad y(-1)= y(1)= 0, \] where \(p> q> -1\), and \(\lambda> 0\) is a positive parameter. He gives a complete study to the exact number of positive solutions to the above problem. The proofs are based upon the time-maps estimate.
Reviewer: Ruyun Ma (Lanzhou)

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47J15 Abstract bifurcation theory involving nonlinear operators
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