Displaying similar documents to “Solutions of the Dirac-Fock equations without projector”

On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length

Eduard Feireisl (1988)

Aplikace matematiky

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The author examined non-zero T -periodic (in time) solutions for a semilinear beam equation under the condition that the period T is an irrational multiple of the length. It is shown that for a.e. T ∈ R 1 (in the sense of the Lebesgue measure on R 1 ) the solutions do exist provided the right-hand side of the equation is sublinear.

Bulk superconductivity in Type II superconductors near the second critical field

Soren Fournais, Bernard Helffer (2010)

Journal of the European Mathematical Society

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We consider superconductors of Type II near the transition from the ‘bulk superconducting’ to the ‘surface superconducting’ state. We prove a new L ∞ estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty [AS].

Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

Silvia Cingolani, Giuseppina Vannella (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We present critical groups estimates for a functional f defined on the Banach space W 0 1 , p ⁢ Ω , Ω bounded domain in R N , 2 < p < ∞ , associated to a quasilinear elliptic equation involving p -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of f in each critical point, we compute the critical groups of f in each isolated critical point via Morse index.

A min-max theorem for multiple integrals of the Calculus of Variations and applications

David Arcoya, Lucio Boccardo (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we deal with the existence of critical points for functionals defined on the Sobolev space W 0 1 , 2 ⁢ Ω by J ⁢ v = ∫ Ω I ⁢ x , v , D ⁢ v ⁢ d ⁢ x , v ∈ W 0 1 , 2 ⁢ Ω , where Ω is a bounded, open subset of R N . Since the differentiability can fail even for very simple examples of functionals defined through multiple integrals of Calculus of Variations, we give a suitable version of the Ambrosetti-Rabinowitz Mountain Pass Theorem, which enables us to the study of critical points for functionals which are not differentiable in all directions....

Positive periodic solutions of functional differential equations with infinite delay

Changxiu Song (2008)

Annales Polonici Mathematici

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The author applies a generalized Leggett-Williams fixed point theorem to the study of the nonlinear functional differential equation x ' ( t ) = - a ( t , x ( t ) ) x ( t ) + f ( t , x t ) . Sufficient conditions are established for the existence of multiple positive periodic solutions.

Periodic solutions for first order neutral functional differential equations with multiple deviating arguments

Lequn Peng, Lijuan Wang (2014)

Annales Polonici Mathematici

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We consider first order neutral functional differential equations with multiple deviating arguments of the form ( x ( t ) + B x ( t - δ ) ) ' = g ₀ ( t , x ( t ) ) + ∑ k = 1 n g k ( t , x ( t - τ k ( t ) ) ) + p ( t ) . By using coincidence degree theory, we establish some sufficient conditions on the existence and uniqueness of periodic solutions for the above equation. Moreover, two examples are given to illustrate the effectiveness of our results.