8,835 research outputs found
On the covering dimension of the set of solutions of some nonlinear equations
No full textWe prove an abstract theorem whose sole hypothesis is that the degree of a certain map is nonzero and whose parametric equations are studied using cohomological mconclusions imply sharp, multidimensional continuation results. Applications are given to nonlinear partial differential equations
Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems.
No full textWe develop an integer valued degree theory for quasilinear Fredholm maps. This class of maps is large enough so we can place in this framework all fully nonlinear elliptic
boundary value problems with smooth enough coefficients.
We use the degree theory in order to obtain multiplicity and bifurcation results for solutions of nonlinear BVP
Spectral flow and bifurcation of critical points of strongly indefinite functionals. II. Bifurcation of periodic orbits of Hamiltonian systems
No full textOur main results here are as follows: Let X* be a family of 2?-periodic Hamiltonian vectorfields that depend smoothly on a real parameter * in [a, b] and has a known, trivial, branch s* of 2?-periodic solutions. Let P* be the Poincare map of the linearization of X* at s* . If the ConleyZehnder index of the path P* does not vanish, then any neighborhood of the trivial branch of periodic solutions contains 2?-periodic solutions not on the branch. Moreover, if each solution s* is constant and each linearization A* of X* at s* is time independent, then bifurcation of 2?-periodic orbits from the branch of equilibria arises whenever i(Ab){i(Ab), where i(A) is the index of the linear Hamiltonian system Ju*=Au
Spectral flow and bifurcation of critical points of strongly indefinite functionals I
No full textSpectral flow is a well-known homotopy invariant of paths of self-adjoint Fredholm operators. We describe here a new construction of this invariant and prove the following theorem: Let f : I × U -> R be a C2 function defined on the product of a real interval I = [a, b] with a neighborhood U of the origin of a real separable Hilbert space H and such that for each t in I, 0 is a critical point of the functional f (t, ·). Assume that the Hessian L of f at 0 is Fredholm and moreover that L_a and L_b are nonsingular. If the spectral flow of the path L does not vanish, then the interval I contains at least one bifurcation point from the trivial branch for solutions of the equation Grad f (t, x) = 0. Equivalently: every neighborhood of I × {0} contains points of the form (t,x) where x is a critical point of f_t different from 0
Enlightenment and Dissent, N° 2, 1983. Éd. par M. Fitzpatrick et D. O. Thomas
No full textBaridon Michel. Enlightenment and Dissent, N° 2, 1983. Éd. par M. Fitzpatrick et D. O. Thomas. In: Dix-huitième Siècle, n°16, 1984. D'Alembert. p. 420
Enlightenment and Dissent, N° 2, 1983. Éd. par M. Fitzpatrick et D. O. Thomas
No full textBaridon Michel. Enlightenment and Dissent, N° 2, 1983. Éd. par M. Fitzpatrick et D. O. Thomas. In: Dix-huitième Siècle, n°16, 1984. D'Alembert. p. 420
Uniqueness of spectral flow
No full textTo each path of self-adjoint Fredholm operators acting on a real separable Hilbert
space H with invertible ends, there is associated an integer called spectral flow. The purpose of this brief note is to show that spectral flow is uniquely characterized by four elementary properties: normalization, continuity, additivity over direct sums, and its value as the difference of the Morse indices of the ends when H is finite dimensional. The proof of uniqueness relies of the invarianceof spectral flow of the path under cogredient transformations of the path
Global several parameter bifurcation and continuation theorems: A unified approach via complementing maps.
No full textWe use the concept of complementing map in order to present a unified approach to the continuation principle, global implicit function theorem and global bifurcation results for compact vector fields depending on several parameters
Schwertmannite formation and properties in acidic drain environments following exposure and oxidation of acid sulfate soils in irrigation areas during extreme drought
No full textAbstract not availableR.W. Fitzpatrick, L.M. Mosley, M.D. Raven, P. Shan
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