A priori bounds, nodal equilibria and connecting orbits in indefinite superlinear parabolic problems
From MaRDI portal
Publication:3508027
DOI10.1090/S0002-9947-08-04404-8zbMath1143.37049OpenAlexW2045935051MaRDI QIDQ3508027
Nils Ackermann, Pavol Quittner, Thomas J. Bartsch, Petr Kaplický
Publication date: 27 June 2008
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9947-08-04404-8
a priori boundsconnecting orbitsexistence results for equilibriaindefinite superlinear parabolic problems
Semigroups of nonlinear operators (47H20) Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)
Related Items
Liouville theorem and a priori estimates of radial solutions for a non-cooperative elliptic system, On variational characterization of four-end solutions of the Allen-Cahn equation in the plane, Excluding blowup at zero points of the potential by means of Liouville-type theorems, Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations, Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation, Boundedness and stability of global solutions for some superlinear and nonautonomous heat equations, Sign-changing solutions of nonlinear elliptic equations, Global dynamic bifurcation of local semiflows and nonlinear evolution equations, Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems, A priori estimates for global solutions of semilinear heat equations in \(\mathbb R^n\), On the heat flow for the two-dimensional Gelfand equation, A priori bounds and complete blow up of positive solutions of indefinite superlinear parabolic problems, Morse theory for indefinite nonlinear elliptic problems, The blow-up rate for positive solutions of indefinite parabolic problems and related Liouville type theorems, Superstable manifolds of semilinear parabolic problems, Biological control via ``ecological damping: an approach that attenuates non-target effects
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Complete and energy blow-up in indefinite superlinear parabolic problems
- On the asymptotic behavior of solutions of certain quasilinear parabolic equations
- A bound for global solutions of semilinear heat equations
- The homotopy index and partial differential equations
- Semilinear evolution equations in Banach spaces
- Critical point theory and Hamiltonian systems
- A priori bounds and multiple solutions for superlinear indefinite elliptic problems
- Superlinear indefinite elliptic problems and Pohozyaev type identities
- Parabolic problems with nonlinear boundary conditions and critical nonlinearities
- On semilinear elliptic equations with indefinite nonlinearities
- Superlinear indefinite elliptic problems and nonlinear Liouville theorems
- Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations
- On the existence of sign changing solutions for semilinear Dirichlet problems
- On the Morse indices of sign changing solutions of nonlinear elliptic problems
- Indefinite elliptic problems in a domain
- Mountain pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems
- Infinite dimensional Morse theory and multiple solution problems
- The generalized Conley index and multiple solutions of semilinear elliptic problems
- Applications of local linking to critical point theory
- Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
- A note on additional properties of sign changing solutions to superlinear elliptic equations
- Dirichlet problem with indefinite nonlinearities
- Multiple equilibria, periodic solutions and a priori bounds for solutions in superlinear parabolic problems
- Variational methods for indefinite superlinear homogeneous elliptic problems
- Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking
- A nonlinear heat equation with singular initial data
- Minimax theorems
- Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations
- Homotopy theory of infinite dimensional manifolds
- Superstable manifolds of semilinear parabolic problems
- Solutions globales d'equations de la chaleur semi lineaires.
- Optimal Control Problems with Final Observation Governed by Explosive Parabolic Equations
- A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain-Pass Theorem
- A priori bounds for positive solutions of nonlinear elliptic equations
- Blow up rate for semilinear heat equations with subcritical nonlinearity
- Critical point theory on partially ordered Hilbert spaces
- Linking type solutions for elliptic equations with indefinite nonlinearities up to the critical growth
