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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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