On the oscillations of the solution curve for a class of semilinear equations

DOI10.1016/j.jmaa.2005.08.074zbMath1160.35404OpenAlexW1989297374MaRDI QIDQ2496682

Philip Korman, Yi Li, Anahit Galstian

Publication date: 20 July 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.08.074

zbMATH Keywords

bifurcationmultiplicity of solutionsoscillatory integrals

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Abstract bifurcation theory involving nonlinear operators (47J15)

Related Items (16)

Stability and instability of solutions of semilinear problems ⋮ Unnamed Item ⋮ Global behavior of bifurcation curves for the nonlinear eigenvalue problems with periodic nonlinear terms ⋮ Infinitely many stability switches in a problem with sublinear oscillatory boundary conditions ⋮ Oscillatory bifurcation problems for ODEs with logarithmic nonlinearity ⋮ On the evolution and qualitative behaviors of bifurcation curves for a boundary value problem ⋮ Infinitely many solutions for a class of resonant problems ⋮ Classification and evolution of bifurcation curves for the one-dimensional Minkowski-curvature problem and its applications ⋮ On the evolution and qualitative behaviors of bifurcation curves for a boundary value problem. II ⋮ Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations. II ⋮ Simple proof of stationary phase method and application to oscillatory bifurcation problems ⋮ INFINITE RESONANT SOLUTIONS AND TURNING POINTS IN A PROBLEM WITH UNBOUNDED BIFURCATION ⋮ Asymptotic oscillations of global solution branches for nonlinear problems ⋮ Asymptotic behavior and global structure of oscillatory bifurcation diagrams ⋮ Global and local structures of oscillatory bifurcation curves ⋮ Asymptotic length of bifurcation curves related to inverse bifurcation problems

Cites Work

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• Bifurcation from simple eigenvalues
• Infinitely many positive solutions of semilinear elliptic problems via sub- and supersolutions
• On the exactness of an S-shaped bifurcation curve
• An Exact Multiplicity Result for a class of Semilinear Equations
• Exact multiplicity results for boundary value problems with nonlinearities generalising cubic

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