Positive and nodal solutions bifurcating from the infinity for a semilinear equation: solutions with compact support

DOI10.4171/PM/1962zbMath1342.35111OpenAlexW1730345000MaRDI QIDQ296841

F. Blanchet-Sadri, M. Dambrine

Publication date: 23 June 2016

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/pm/1962

zbMATH Keywords

Schrödinger equationnonlinear eigenvalue problemsasymptotic bifurcationbranches of nodal solutionsflat solutionsinfinite well potentialphase plane methodssolutions with compact supportvariational and topological methods

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Bifurcation theory for ordinary differential equations (34C23) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Degree theory for nonlinear operators (47H11) PDEs in connection with quantum mechanics (35Q40) Free boundary problems for PDEs (35R35) Semilinear elliptic equations (35J61)

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Beyond the classical strong maximum principle: sign-changing forcing term and flat solutions ⋮ On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via singular potentials: the multi-dimensional case ⋮ Linearized stability for degenerate and singular semilinear and quasilinear parabolic problems: the linearized singular equation ⋮ Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for \(N \geq 3\)

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