5-Shaped Bifurcation Curves of Nonlinear Elliptic Boundary Value Problems.
A bifurcation theorem for noncoercive integral functionals
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
A bifurcation theory for some nonlinear elliptic equations
We deal with the problem ⎧ -Δu = f(x,u) + λg(x,u), in Ω, ⎨ () ⎩ 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 () admits a non-zero, non-negative strong solution such that for all p ≥ 2. Moreover, the function is negative and decreasing in ]0,λ*[, where is the energy functional related to ().
A Class of Elliptic Partial Differential Equations with Exponential Nonlinearities.
A double -shaped bifurcation curve for a reaction-diffusion model with nonlinear boundary conditions.
A global bifurcation result of a Neumann problem with indefinite weight.
A global branch of steady vortex rings.
A global continuation theorem for obtaining eigenvalues and bifurcation points
A global solution curve for a class of semilinear equations.
A Hopf bifurcation generated by variation of the domain
A Hopf bifurcation of interfaces in a Dirichlet problem.
A hybrid neural network model for the dynamics of the Kuramoto-Sivashinsky equation.
A note on the bifurcation of solutions for an elliptic sublinear problem
A note to a bifurcation result of H. Kielhöfer for the wave equation
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
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 that differ by an angle . 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.
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 -Laplacian.
A Variational Approach to Bifurcation in Lp on an Unbounded Symmetrical Domain.
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
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...