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

Patrick Habets, Marcellino Gaudenzi

DOI: http://dx.doi.org/10.12775/TMNA.1999.024

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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