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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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##### References:
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