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Calculus of Variations and Partial Differential Equations : Volume 56

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Calculus of Variations and Partial Differential Equations : Volume 54

Calculus of Variations and Partial Differential Equations : Volume 54, Issue 4, December 2015

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Singular Poisson equations on Finsler–Hadamard manifolds

Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities

Bubbling solutions for the Chern–Simons gauged $$O(3)$$ sigma model on a torus

Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle

Nonexistence results for elliptic differential inequalities with a potential on Riemannian manifolds

Multiple positive solutions for Schrödinger systems with mixed couplings

Semmes family of curves and a characterization of functions of bounded variation in terms of curves

Nonlinear gradient estimates for elliptic equations in quasiconvex domains

Addendum to the paper: Nonlinear gradient estimates for elliptic equations in quasiconvex domains

Subsequent singularities in mean-convex mean curvature flow

A non-squeezing theorem for convex symplectic images of the Hilbert ball

Stochastic homogenization of a nonconvex Hamilton–Jacobi equation

Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level

Monotonicity formulas for obstacle problems with Lipschitz coefficients

Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex

Discrete-time gradient flows and law of large numbers in Alexandrov spaces

Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications

Hyperelasticity as a $$\Gamma $$ -limit of peridynamics when the horizon goes to zero

Addendum to the paper: Hyperelasticity as a $$\Gamma $$ -limit of peridynamics when the horizon goes to zero

Existence of solitary waves for supercritical Schrödinger systems in dimension two

Regularity and long-time behavior of nonlocal heat flows

Semicontinuity of eigenvalues under intrinsic flat convergence

Aleksandrov-Fenchel inequalities for unitary valuations of degree $$2$$ and $$3$$

On some nonlinear elliptic PDEs with Sobolev–Hardy critical exponents and a Li–Lin open problem

Renormalized solutions to the continuity equation with an integrable damping term

Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity

Non-unique conical and non-conical tangents to rectifiable stationary varifolds in $$\mathbb R^4$$

Foliations by stable spheres with constant mean curvature for isolated systems without asymptotic symmetry

Mean curvature bounds and eigenvalues of Robin Laplacians

Gap solitons in almost periodic one-dimensional structures

Convex hypersurfaces evolving by volume preserving curvature flows

Translating solitons of the mean curvature flow

Singularities of the nodal set of segregated configurations

Large-time behavior for obstacle problems for degenerate viscous Hamilton–Jacobi equations

Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition

Every point in a Riemannian manifold is critical

Stationary Kirchhoff systems in closed $$3$$ -dimensional manifolds

Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies

Capillary surfaces inside polyhedral regions

Multiple valued maps into a separable Hilbert space that almost minimize their $$p$$ Dirichlet energy or are squeeze and squash stationary

Properties of a frequency of Almgren type for harmonic functions in Carnot groups

Nodal sets of Steklov eigenfunctions

Boundary regularity for the supercritical Lane-Emden heat flow

Erratum to: Boundary regularity for the supercritical Lane-Emden heat flow

Semi-classical standing waves for nonlinear Schrödinger systems

Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions

Stability of non compact steady and expanding gradient Ricci solitons

Geometric barriers for the existence of hypersurfaces with prescribed curvatures in M $$^n\times $$ R

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Gap solitons in almost periodic one-dimensional structures

Content Provider	Springer Nature Link
Author	Pankov, Alexander
Copyright Year	2015
Abstract	We consider almost periodic stationary nonlinear Schrödinger equations in dimension 1. Under certain assumptions we prove the existence of nontrivial finite energy solutions in the strongly indefinite case. The proof is based on a carefull analysis of the energy functional restricted to the so-called generalized Nehari manifold, and the existence and fine properties of special Palais–Smale sequences. As an application, we show that certain one dimensional almost periodic photonic crystals possess gap solitons for all prohibited frequencies.
Ending Page	1984
Page Count	22
Starting Page	1963
File Format	PDF
ISSN	09442669
e-ISSN	14320835
Journal	Calculus of Variations and Partial Differential Equations
Issue Number	2
Volume Number	54
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-03-31
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Homoclinic and heteroclinic solutions PDEs in connection with optics and electromagnetic theory Composite media; random media Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics 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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