Benjamin–Ono periodic bifurcating water waves in presence of an essential spectrum
Bifurcating solutions to the monodomain model equipped with FitzHugh-Nagumo kinetics.
Bifurcation analysis of stimulated Brillouin scattering
Bifurcation and multiplicity results for a nonhomogeneous semilinear elliptic problem.
Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
Bifurcation de Hopf d’ondes de choc pour les équations de Navier-Stokes compressible
Bifurcation for a semilinear elliptic equation on Rn with radially symmetric coefficients.
Bifurcation for Monge-Ampère Equations on Flat Tori.
Bifurcation for nonlinear elliptic boundary value problems I.
This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the...
Bifurcation for odd nonlinear elliptic variational inequalities
Bifurcation in the solution set of the von Kármán equations of an elastic disk lying on an elastic foundation
We investigate bifurcation in the solution set of the von Kármán equations on a disk Ω ⊂ ℝ² with two positive parameters α and β. The equations describe the behaviour of an elastic thin round plate lying on an elastic base under the action of a compressing force. The method of analysis is based on reducing the problem to an operator equation in real Banach spaces with a nonlinear Fredholm map F of index zero (to be defined later) that depends on the parameters α and β. Applying the implicit function...
Bifurcation of free vibrations for completely resonant wave equations
We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent.
Bifurcation of reaction-diffusion systems related to epidemics.
Bifurcation of stationary solutions to quasivariational inequalities
Bifurcation and eigenvalue theorems are proved for a certain type of quasivariational inequalities using the method of a jump in the Leray-Schauder degree.
Bifurcation points of reaction-diffusion systems with unilateral conditions
Bifurcation results for a class of perturbed Fredholm maps.
Bifurcation theorems for nonlinear problems with lack of compactness
We deal with a bifurcation result for the Dirichlet problem ⎧ a.e. in Ω, ⎨ ⎩. Starting from a weak lower semicontinuity result by E. Montefusco, which allows us to apply a general variational principle by B. Ricceri, we prove that, for μ close to zero, there exists a positive number such that for every the above problem admits a nonzero weak solution in satisfying .
Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order
This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained are similar...