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5-Shaped Bifurcation Curves of Nonlinear Elliptic Boundary Value Problems.

Henning Wiebers (1985)

Mathematische Annalen

A bifurcation theorem for noncoercive integral functionals

Francesca Faraci (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the existence of critical points for noncoercive functionals, whose principal part has a degenerate coerciveness. A bifurcation result at zero for the associated differential operator is established.

A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations

Walter Craig (1983)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A bifurcation theory for some nonlinear elliptic equations

Biagio Ricceri (2003)

Colloquium Mathematicae

We deal with the problem ⎧ -Δu = f(x,u) + λg(x,u), in Ω, ⎨ ( $P_{λ}$ ) ⎩ $u_{∣ \partial Ω} = 0$ where Ω ⊂ ℝⁿ is a bounded domain, λ ∈ ℝ, and f,g: Ω×ℝ → ℝ are two Carathéodory functions with f(x,0) = g(x,0) = 0. Under suitable assumptions, we prove that there exists λ* > 0 such that, for each λ ∈ (0,λ*), problem ( $P_{λ}$ ) admits a non-zero, non-negative strong solution $u_{λ} \in ⋂_{p \geq 2} W^{2, p} (Ω)$ such that $l i m_{λ \to 0 ⁺} | | u_{λ} {| |}_{W^{2, p} (Ω)} = 0$ for all p ≥ 2. Moreover, the function $λ \mapsto I_{λ} (u_{λ})$ is negative and decreasing in ]0,λ*[, where $I_{λ}$ is the energy functional related to ( $P_{λ}$ ).

A Class of Elliptic Partial Differential Equations with Exponential Nonlinearities.

Pierre A. Vuillermot (1984)

Mathematische Annalen

A double $S$ -shaped bifurcation curve for a reaction-diffusion model with nonlinear boundary conditions.

Goddard, Jerome II, Lee, Eun Kyoung, Shivaji, R. (2010)

Boundary Value Problems [electronic only]

A global bifurcation result of a Neumann problem with indefinite weight.

El Khalil, Abdelouahed, Ouanan, Mohammed (2004)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

A global branch of steady vortex rings.

C.J. Amick, R.E.L. Turner (1988)

Journal für die reine und angewandte Mathematik

A global continuation theorem for obtaining eigenvalues and bifurcation points

Milan Kučera (1988)

Czechoslovak Mathematical Journal

A global solution curve for a class of semilinear equations.

Korman, Philip (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A Hopf bifurcation generated by variation of the domain

Vegas, José M. (1982)

Portugaliae mathematica

A Hopf bifurcation of interfaces in a Dirichlet problem.

Ham, YoonMee, Lee, Sang-Gu (1999)

Southwest Journal of Pure and Applied Mathematics [electronic only]

A hybrid neural network model for the dynamics of the Kuramoto-Sivashinsky equation.

Smaoui, Nejib (2004)

Mathematical Problems in Engineering

A note on the bifurcation of solutions for an elliptic sublinear problem

Alessio Porretta (2002)

Rendiconti del Seminario Matematico della Università di Padova

A note to a bifurcation result of H. Kielhöfer for the wave equation

Otto Vejvoda, Pavel Krejčí (1991)

Mathematica Bohemica

A modification of a classical number-theorem on Diophantine approximations is used for generalizing H. kielhöfer's result on bifurcations of nontrivial periodic solutions to nonlinear wave equations.

A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types

Lucas Döring, Radu Ignat, Felix Otto (2014)

Journal of the European Mathematical Society

We study the Landau-Lifshitz model for the energy of multi-scale transition layers – called “domain walls” – in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors $m_{α}^{\pm} \in 𝕊^{2}$ that differ by an angle $2 α$ . Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The...

A remark on perturbed elliptic equations of Caffarelli-Kohn-Nirenberg type.

Boumediene Abdellaoui, Veronica Felli, Ireneo Peral (2005)

Revista Matemática Complutense

Using a perturbation argument based on a finite dimensional reduction, we find positive solutions to a given class of perturbed degenerate elliptic equations with critical growth.

A result on the bifurcation from the principal eigenvalue of the $A p$ -Laplacian.

Drábek, P., Elkhalil, A., Touzani, A. (1997)

Abstract and Applied Analysis

A Variational Approach to Bifurcation in Lp on an Unbounded Symmetrical Domain.

C.A. Stuart (1983)

Mathematische Annalen

A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions

Jamol I. Baltaev, Milan Kučera, Martin Väth (2012)

Applications of Mathematics

We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential...

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