A shooting argument with oscillation for semilinear elliptic radially symmetric equations

DOI10.1017/S0308210500026603zbMath0671.35028MaRDI QIDQ3824756

H. Plakties, Christopher K. R. T. Jones, Tassilo Kuepper

Publication date: 1988

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

zbMATH Keywords

existenceshooting methodnodal propertiesgrowth propertiessemilinearRadially symmetricbounds for the solutionscascade of solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear boundary value problems for ordinary differential equations (34B15) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (5)

An instability mechanism for radially symmetric standing waves of a nonlinear Schrödinger equation ⋮ Constructive proofs for localised radial solutions of semilinear elliptic systems on Rd ⋮ Planar radial spots in a three-component FitzHugh-Nagumo system ⋮ INFINITELY MANY NODAL SOLUTIONS FOR A WEAKLY COUPLED NONLINEAR SCHRÖDINGER SYSTEM ⋮ Some existence and bifurcation results for solutions of nonlinear Sturm- Liouville eigenvalue problems

Cites Work

• Uniqueness of positive solutions of semilinear equations in \(R^ n\).
• Nodal properties and variational characterizations of solutions to nonlinear Sturm-Liouville problems
• Nodal properties and bifurcation from the essential spectrum for a class of nonlinear Sturm-Liouville problems
• Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems
• Existence of solitary waves in higher dimensions
• Boundary value problems for a class of nonlinear differential equations
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
• On the Infinitely Many Solutions of a Semilinear Elliptic Equation
• Unnamed Item

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