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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 43
  3. Calculus of Variations and Partial Differential Equations : Volume 43, Issue 1-2, January 2012
  4. On the existence of nonlinear Dirac-geodesics on compact manifolds
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 43, Issue 3-4, March 2012
Calculus of Variations and Partial Differential Equations : Volume 43, Issue 1-2, January 2012
Boundary regularity for minimizers of the micromagnetic energy functional
The Bernstein theorem for a class of fourth order equations
Extension of a theorem of Shi and Tam
On the solutions to a Liouville-type system involving singularity
On the existence of nonlinear Dirac-geodesics on compact manifolds
Monotonicity and one-dimensional symmetry for solutions of −Δ p u = f(u) in half-spaces
New Korn-type inequalities and regularity of solutions to linear elliptic systems and anisotropic variational problems involving the trace-free part of the symmetric gradient
The canonical shrinking soliton associated to a Ricci flow
Volume preserving mean curvature flow of revolution hypersurfaces between two equidistants
Differential forms in Carnot groups: a Γ-convergence approach
Existence of solutions for quasilinear elliptic equations with jumping nonlinearities under the Neumann boundary condition
Regularity of mean curvature flows with Neumann free boundary conditions
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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On the existence of nonlinear Dirac-geodesics on compact manifolds

Content Provider SpringerLink
Author Isobe, Takeshi
Copyright Year 2011
Abstract We show that for super-linear nonlinearity, there exists a “non-trivial” nonlinear Dirac-geodesic on $${\mathbb{T}^n_{\Gamma}=\mathbb{R}^n/\Gamma}$$ , a flat tori, in each “bosonic” sector. We also show that for any compact Riemannian manifold with “bumpy” metric, there exists a non-trivial nonlinear Dirac-geodesic in each bosonic sector if the nonlinearity is cubic or super-cubic and “large”. Our proof is based on critical point theory, in particular, a generalized linking argument applied to a strongly indefinite functional on a fibered Hilbert manifold.
Ending Page 121
Page Count 39
Starting Page 83
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 1-2
Volume Number 43
Language English
Publisher Springer-Verlag
Publisher Date 2011-02-17
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Applications to the theory of geodesics (problems in one independent variable) Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Supersymmetry and quantum mechanics Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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