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

Mathematische Annalen

### A bifurcation theorem for noncoercive integral functionals

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### A bifurcation theory for some nonlinear elliptic equations

Colloquium Mathematicae

We deal with the problem ⎧ -Δu = f(x,u) + λg(x,u), in Ω, ⎨ (${P}_{\lambda }$) ⎩ ${u}_{\mid \partial \Omega }=0$ 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 (${P}_{\lambda }$) admits a non-zero, non-negative strong solution ${u}_{\lambda }\in {\bigcap }_{p\ge 2}{W}^{2,p}\left(\Omega \right)$ such that $li{m}_{\lambda \to 0⁺}||{u}_{\lambda }{||}_{{W}^{2,p}\left(\Omega \right)}=0$ for all p ≥ 2. Moreover, the function $\lambda ↦{I}_{\lambda }\left({u}_{\lambda }\right)$ is negative and decreasing in ]0,λ*[, where ${I}_{\lambda }$ is the energy functional related to (${P}_{\lambda }$).

### A Class of Elliptic Partial Differential Equations with Exponential Nonlinearities.

Mathematische Annalen

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

Boundary Value Problems [electronic only]

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

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

### A global branch of steady vortex rings.

Journal für die reine und angewandte Mathematik

### A global continuation theorem for obtaining eigenvalues and bifurcation points

Czechoslovak Mathematical Journal

### A global solution curve for a class of semilinear equations.

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

### A Hopf bifurcation generated by variation of the domain

Portugaliae mathematica

### A Hopf bifurcation of interfaces in a Dirichlet problem.

Southwest Journal of Pure and Applied Mathematics [electronic only]

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

Mathematical Problems in Engineering

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

Rendiconti del Seminario Matematico della Università di Padova

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

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

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 ${m}_{\alpha }^{±}\in {𝕊}^{2}$ that differ by an angle $2\alpha$. 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.

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 $Ap$-Laplacian.

Abstract and Applied Analysis

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

Mathematische Annalen

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

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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