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lyapunov-schmidt reduction (184) 184
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Journal of Computational and Nonlinear Dynamics, ISSN 1555-1415, 09/2016, Volume 11, Issue 5
Lyapunov-Schmidt reduction is one of the powerful and significant methods to simplify nonlinear ordinary differential systems (ODSs) with standard formulation.... 
fractional differential equation | Fredholm operator | Lyapunov-Schmidt reduction | Caputo derivative | MECHANICS | BIFURCATION | ENGINEERING, MECHANICAL | Formulations | Nonlinear dynamics | Reduction | Computation | Nonlinearity | Derivatives | Dynamical systems | Standards
Journal Article
Nonlinearity, ISSN 0951-7715, 08/2017, Volume 30, Issue 9, pp. 3560 - 3586
In this work we first provide sufficient conditions to assure the persistence of some zeros of functions having the form g(z, epsilon) - g(0) (z) +... 
periodic solution | limit cycle | Lyapunov-Schimidt reduction | bifurcation theory | nonlinear differential system | AVERAGING THEORY | MATHEMATICS, APPLIED | SMALL-PARAMETER | PHYSICS, MATHEMATICAL | BIFURCATION | Mathematics - Dynamical Systems
Journal Article
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, ISSN 1120-6330, 2018, Volume 29, Issue 1, pp. 1 - 29
We consider the finite dimensional reduction of the well known non-equilibrium thermodynamics theory developed through the last two decades by a team of... 
Morse theory | Non-equilibrium thermodynamics | Collective variables | Reaction-diffusion system | Lyapunov–Schmidt reduction | MATHEMATICS | MATHEMATICS, APPLIED | Lyapunov-Schmidt reduction | reaction-diffusion system | collective variables
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2016, Volume 260, Issue 1, pp. 781 - 817
The dynamics of a diffusive Lotka–Volterra type model for two species with nonlocal delay effect and Dirichlet boundary conditions is investigated in this... 
Nonlocal delay | Hopf bifurcation | Lyapunov–Schmidt reduction | Reaction–diffusion | MATHEMATICS | Reaction diffusion | STABILITY | Lyapunov Schmidt reduction | EQUATIONS | POPULATION-MODEL
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 2012, Volume 17, Issue 6, pp. 2201 - 2223
In this paper, we use the method of characteristics to study singularities in the flow of a parameterized family of extremals for an optimal control problem.... 
Lyapunov-schmidt reduction | Maximum principle | Optimal control | Fold and simple cusp singularities | MATHEMATICS, APPLIED | HAMILTON-JACOBI-BELLMAN | fold and simple cusp singularities | Lyapunov-Schmidt reduction | SUFFICIENT CONDITIONS | FAMILIES | maximum principle | EXTREMALS
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2014, Volume 263, pp. 14 - 24
The purpose of this manuscript is to study the dynamics of a damped harmonic oscillator with delayed feedback. Different to previous papers, the bifurcation... 
Non-semisimple eigenvalues | [formula omitted]-equivariant | Hopf bifurcation | Lyapunov–Schmidt reduction | Harmonic oscillator | equivariant | Lyapunov-Schmidt reduction | MATHEMATICS, APPLIED | RESONANCE | Lyapunov Schmidt reduction | S-1-equivariant
Journal Article
Advances in Nonlinear Analysis, ISSN 2191-9496, 08/2018, Volume 7, Issue 3, pp. 385 - 405
By a perturbative argument, we construct solutions for a plasma-type problem with two opposite-signed sharp peaks at levels 1 and , respectively, where . We... 
plasma problem | 35J20 | free boundaries | 35J60 | 82D10 | Lyapunov–Schmidt reduction | Peak solutions | Lyapunov-Schmidt reduction | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | VORTICES | CONCENTRATING SOLUTIONS | NONLINEAR EIGENVALUE PROBLEM | EQUATION | 2 DIMENSIONS
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2017, Volume 35, pp. 441 - 456
In this paper, we consider the two similar competing species in a competition unstirred chemostat model with diffusion. The two competing species are assumed... 
Stability | Chemostat | Lyapunov–Schmidt reduction | Existence | MATHEMATICS, APPLIED | Lyapunov-Schmidt reduction | Information science | Analysis
Journal Article
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, ISSN 1417-3875, 2019, Volume 2019, Issue 76, pp. 1 - 16
It is shown that a class of symmetric solutions of the scalar nonlinear functional differential equations at resonance with deviations from R -> R can be... 
MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | solvability | Lyapunov-Schmidt reduction method | symmetric solution | lyapunov–schmidt reduction method
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 01/2017, Volume 73, Issue 2, pp. 310 - 326
This paper is concerned with a stage structure model with spatiotemporal delay and homogeneous Dirichlet boundary condition. The existence of steady state... 
Stage structure model | Dirichlet boundary condition | Lyapunov–Schmidt reduction | Spatiotemporal delay | SYSTEM | MATHEMATICS, APPLIED | Lyapunov-Schmidt reduction | HOPF-BIFURCATION | GROWTH | DYNAMICS | DIFFUSION | POPULATION-MODEL
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 9/2017, Volume 168, Issue 5, pp. 1000 - 1015
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2012, Volume 241, Issue 5, pp. 528 - 533
We deal with nonlinear T -periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions.... 
Periodic solution | Averaging method | Lyapunov–Schmidt reduction | Lyapunov-Schmidt reduction | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Manifolds | Reduction | Perturbation methods | Tools | Bifurcations | Nonlinearity | Mapping | Invariants
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 07/2012, Volume 75, Issue 11, pp. 4315 - 4324
Multiplicity results are proved for the nonlinear elliptic system {−Δu+g(v)=0−Δv+g(u)=0in Ω,u=v=0on ∂Ω, where Ω⊂RN is a bounded domain with smooth boundary and... 
Mountain Pass Theorem | Lyapunov–Schmidt reduction method | Elliptic system | Lyapunov-Schmidt reduction method | MATHEMATICS | MATHEMATICS, APPLIED | Mountains | Reduction | Theorems | Smooth boundaries | Nonlinearity | Joining | Symmetry
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 06/2014, Volume 266, Issue 11, pp. 6531 - 6598
In this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations... 
Asymptotic behavior of least energy solutions | Fractional Laplacian | Lyapunov–Schmidt reduction | Critical nonlinearity | Lyapunov-Schmidt reduction | BUBBLE | INEQUALITY | EQUATIONS | TOWER | EXTENSION PROBLEM | MATHEMATICS | REGULARITY | HARDY-LITTLEWOOD-SOBOLEV | CRITICAL SOBOLEV EXPONENT | DERIVATIVES | MOVING SPHERES | Energy industry
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2015, Volume 259, Issue 1, pp. 1 - 24
Consider an autonomous ordinary differential equation in Rn that has a homoclinic solution asymptotic to a hyperbolic equilibrium. The homoclinic solution is... 
Codiagonalization of quadratic forms | Exponential dichotomies | Degenerate homoclinic bifurcation | Chaotic motions | Lyapunov–Schmidt reduction | Lyapunov-Schmidt reduction | MATHEMATICS | EQUATIONS | SYSTEMS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 04/2016, Volume 260, Issue 7, pp. 6130 - 6175
We consider the nonlocal KPP-Fisher equation ut(t,x)=uxx(t,x)+u(t,x)(1−(K⁎u)(t,x)) which describes the evolution of population density u(t,x) with respect to... 
Non-monotone positive traveling front | KPP-Fisher nonlocal equation | Periodic solution | Lyapunov–Schmidt reduction | Existence | Uniqueness | Lyapunov-Schmidt reduction | Mathematics - Classical Analysis and ODEs
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 4/2019, Volume 70, Issue 2, pp. 1 - 21
In this paper, we consider the following Kirchhoff problem $$\begin{aligned} -\left( a+b\int \limits _{\mathbb R^3} |\nabla u|^2\mathrm{d}x\right) \Delta... 
Engineering | 35J20 | Mathematical Methods in Physics | Kirchhoff equation | Lyapunov–Schmidt reduction | Infinitely many solutions | 35B40 | Theoretical and Applied Mechanics | EXISTENCE | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | Lyapunov-Schmidt reduction
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 07/2016, Volume 72, Issue 1, pp. 147 - 177
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 07/2015, Volume 308, pp. 59 - 79
Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or “cellular instability”, of... 
Viscous shock waves | Hopf bifurcation | Lyapunov–Schmidt reduction | Lyapunov-Schmidt reduction | MATHEMATICS, APPLIED | PROFILES | INSTABILITY | PHYSICS, MULTIDISCIPLINARY | INVISCID STABILITY | SYSTEMS | PHYSICS, MATHEMATICAL
Journal Article
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