Bifurcation from a homoclinic orbit in parabolic differential equations

DOI10.1017/S0308210500018916zbMath0636.35010OpenAlexW2096695703MaRDI QIDQ3775885

C. Miguel Blázquez

Publication date: 1986

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/s0308210500018916

zbMATH Keywords

periodic orbithomoclinic orbitsectorial operatorsinfinite dimensional

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Perturbations in context of PDEs (35B20) Bifurcations in context of PDEs (35B32) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (11)

Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation ⋮ Chaos in infinite dimensions: a generalization of a theorem of Sil'nikov ⋮ The existences of transverse homoclinic solutions and chaos for parabolic equations ⋮ Using Melnikov's method to solve Silnikov's problems ⋮ Persistence of bounded solutions to degenerate Sobolev-Galpern equations ⋮ Bounded solutions for non-autonomous parabolic equations ⋮ Computation of bifurcation manifolds of linearly independent homoclinic orbits ⋮ Multiple homoclinic solutions for singular differential equations ⋮ Linearly independent homoclinic bifurcations parameterized by a small function ⋮ The periodic solutions bifurcated from a homoclinic solution for parabolic differential equations ⋮ Bifurcation from homoclinic to periodic solutions in singular ordinary differential equations

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• An example of bifurcation to homoclinic orbits
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
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