Applications of phase plane analysis of a Liénard system to positive solutions of Schrödinger equations

DOI10.1090/S0002-9939-02-06681-9zbMath1107.35050MaRDI QIDQ4779855

Naoto Yamaoka, Jitsuro Sugie

Publication date: 28 October 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Liénard systemSchrödinger equationpositive solutionexterior domain

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (4)

Positive solutions for second-order nonlinear differential equations ⋮ The continuous dependence on parameters of solutions for a class of elliptic problems on exterior domains ⋮ A note on positive evanescent solutions for a certain class of elliptic problems ⋮ Existence of global positive solutions of semilinear elliptic equations

Cites Work

• Unnamed Item
• Positive solutions of Schrödinger equations in two-dimensional exterior domains
• Positive solutions of quasilinear elliptic equations in exterior domains
• Criteria for oscillatory sublinear Schrödinger equations
• On global asymptotic stability of systems of Liénard type
• Nonoscillation theorems for a nonlinear self-adjoint differential equation.
• On the equation \(x +f(x)h(x')x' +g(x) = e(t)\)
• On the generalized Lienard equation with negative damping
• Oscillation constant of second-order nonlinear self-adjoint differential equations
• Bounded Positive Solutions of Semilinear Schrödinger Equations

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