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Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems. (English) Zbl 0607.34012
The discussion in this paper centers around the singular nonlinear Dirichlet problem $$-u''+w(t)| u|^{\sigma}u=\lambda u,$$ $$u(0)=0$$, $$u\in L^ 2[0,\infty)$$, where $$\sigma >0$$ is a constant, and w is a positive continuous function satisfying the minimal growth condition $$\int^{\infty}_{0}w^{-2/\sigma}dt<\infty.$$ After some remarks on free Ljusternik-Schnirelman theory, the author gives applications to abstract nonlinear eigenvalue problems, semilinear elliptic boundary value problems, and to bifurcation theory.
Reviewer: N.L.Maria

##### MSC:
 34A99 General theory for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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