Existence and multiplicity of positive solutions for boundary value problems of 2d order ODE

Patrick Habets, Marcellino Gaudenzi

Abstract


We study the existence and multiplicity of positive solutions of the
boundary value problem
$$
u''+sf(t,u)=0,\quad u(0)=u(1)=0,
$$
where $s$ is a positive parameter and $f$ is a non-negative function.
We indicate examples with more than two solutions.

Keywords


Dirichlet boundary value problem; positive solutions; multiplicity; upper and lower solutions; shooting method; exact count of solutions

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