A note on bifurcation from infinity

A primer on connectivity

Bifurcation from Zero or Infinity in Sturm–Liouville Problems Which Are Not Linearizable

We reexamine bifurcation questions for potential operators. Based on the Conley index theory we present a unified approach to bifurcations both at the origin and at infinity. Our results provide improvements of the existing theory.

background

Notes on the bifurcation theorem

We study a semilinear elliptic equation with an asymptotic linear nonlinearity.
Exact multiplicity of solutions are obtained under various conditions on the
nonlinearity and the spectrum set.
Our method combines a bifurcation approach and Leray-Schauder degree theory.

/pdf/blow-up-points-of-solution-curves-for-a-semilinear-problem-4ka7yvlfax.pdf

Blow up points of solution curves for a semilinear problem

(f2) lim u→∞ f(u) u =f+ ? 0; lim u→−∞ f(u) u =f− ? 0: For the de5niteness, we assume f+ ?f−, and when f+ =f−, we use f± to represent it. We will consider f being either superlinear or sublinear. f is said to be superlinear if f(u)=u is decreasing in (0;∞) and is increasing in (−∞; 0); and f is said to be sublinear if f(u)=u is increasing in (0;∞) and is decreasing in (−∞; 0): The semilinear equation (1.1) with f satisfying (f1), (f2) has been studied extensively since early 1970s. Several di9erent approaches, like variational methods (Morse

result

/pdf/exact-multiplicity-of-solutions-to-superlinear-and-sublinear-551fqfewm5.pdf

A note on bifurcation from infinity

Citations

A primer on connectivity

Bifurcation from Zero or Infinity in Sturm–Liouville Problems Which Are Not Linearizable

Notes on the bifurcation theorem

Blow up points of solution curves for a semilinear problem

Exact multiplicity of solutions to superlinear and sublinear problems

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