Uniqueness of positive solutions of some semilinear Sturm–Liouville problems on the half line

DOI10.1017/S0308210500032042zbMath0545.34013OpenAlexW2322816542MaRDI QIDQ3336075

John F. Toland

Publication date: 1984

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500032042

zbMATH Keywords

Sturm-Liouville problemssemilinearautonomous case

Mathematics Subject Classification ID

Related Items (18)

A global branch of solutions to a semilinear equation on an unbounded interval ⋮ Concentration behavior of ground states for \( L^2\)-critical Schrödinger equation with a spatially decaying nonlinearity ⋮ Blowup of \(H^1\) solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation ⋮ Bifurcation in \(L^ p({\mathbb{R}})\) for a semilinear equation ⋮ Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation ⋮ On the critical norm concentration for the inhomogeneous nonlinear Schrödinger equation ⋮ Finite time/infinite time blow-up behaviors for the inhomogeneous nonlinear Schrödinger equation ⋮ Scattering theory in weighted L2 space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation ⋮ Standing waves with prescribed \(L^2\)-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities ⋮ Graph intersection and uniqueness results for some nonlinear elliptic problems ⋮ Blowup and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrödinger equation ⋮ Global bifurcation analysis and uniqueness for a semilinear problem ⋮ Bifurcation from infinity for an asymptotically linear problem on the half-line ⋮ Bifurcation and Stability of Travelling Waves in Self-focusing Planar Waveguides ⋮ Long Time Dynamics of Nonradial Solutions to Inhomogeneous Nonlinear Schrödinger Equations ⋮ A Uniqueness Result for Δu - λu + V(⃒x⃒)u^P = 0 on ℝ² ⋮ Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions ⋮ Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrödinger equation

Cites Work

• Uniqueness of positive solutions of semilinear equations in \(R^ n\).
• Global bifurcation for Neumann problems without eigenvalues
• Bifurcation for Neumann problems without eigenvalues

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