Results 51 to 60 of about 774 (145)
Some remarks on the Melnikov function
Electronic Journal of Differential Equations, 2002 The authors study the system \[ x'=f(x)+\varepsilon h(t+\alpha,x,\varepsilon), \] where \(\varepsilon\) is a small parameter. It is assumed that if \(\varepsilon=0\), then the system has a nondegenerate homoclinic solution \(\phi(t)\). The Melnikov function \(M(\alpha)\) is studied in the case where \(\phi(t)=\Phi(e^t)\) for a rational function \(\Phi\)
Flaviano Battelli, Michal Feckan
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A generalization of Françoise's algorithm for calculating higher order Melnikov functions
Bulletin des Sciences Mathématiques, 2002 In [J. Differential Equations 146 (2) (1998) 320–335], Françoise gives an algorithm for calculating the first nonvanishing Melnikov function Mℓ of a small polynomial perturbation of a Hamiltonian vector field and shows that Mℓ is given by an Abelian integral.
Jebrane, Ahmed +2 more
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Unlocking Heterobimetallic Architectures in a Symmetric PNNP Ligand Environment
Chemistry – A European Journal, Volume 32, Issue 21, 1 June 2026.A symmetric PNNP ligand enables the modular assembly of heterobimetallic ZnRu and CoRu complexes from a mononuclear Ru(II) precursor. Ligand deprotonation triggers dearomatization and contraction of the metal–metal distance. Combined DFT and QTAIM analyses reveal metallophilic interaction in CoRu but not in ZnRu, highlighting controllable geometric and
Stanislav Melnikov +4 more
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Journal of Cosmetic Dermatology, Volume 25, Issue 6, June 2026.ABSTRACT Background Aesthetic medicine is rapidly expanding, yet lack of standardized educational pathways led many healthcare providers (HCPs) to rely on social media influencers for education. The scientific validity of the information shared, however, remains uncertain.
Giovanni Buzzaccarini +15 more
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Computation of expansion coefficients of Melnikov functions near a nilpotent center
Computers & Mathematics with Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junmin Yang, Maoan Han
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Higher order Melnikov function for a quartic hamiltonian with cuspidal loop
Discrete and Continuous Dynamical Systems, 2002 The authors consider the polynomial perturbations \[ X_{\varepsilon}=X_H+ \varepsilon f(x,y,\varepsilon)\frac{\partial}{\partial x}+ \varepsilon g(x,y,\varepsilon)\frac{\partial}{\partial y}, \] where \(f(x,y,\varepsilon)\) and \(g(x,y,\varepsilon)\) are polynomials in \(x,y\) with coefficients depending analytically on the small parameter ...
Zhao, Yulin, Zhu, Siming
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Melnikov functions and heteroclinic orbits in delay differential equations
Journal of Mathematical Analysis and Applications, 1990 The author gives sufficient conditions for the existence of bounded solutions for the perturbed delay differential equation \(\dot z(t)=g(z_ t)+h(t,z_ t,\epsilon)\) where \(h(t,\phi,0)=0\), \(\epsilon >0\), \(z_ t(\theta)=z(t+\theta)\), \(\theta\in [-r;0]\) with \(r>0\).
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Higher-order Melnikov functions for degenerate cubic Hamiltonians
Advances in Differential Equations, 1996 The author considers quadratic perturbation problems of Hamiltonian systems in the plane with degenerate cubic Hamiltonians. He first uses the scheme of J. P. Francoise to compute explicitly the first four Melnikov functions \(M_1(h),\dots, M_4(h)\), then he proves the following five interesting theorems. Theorem 1.
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Jump and Pull-in Instability of a MEMS Gyroscope Vibrating System. [PDF]
Micromachines (Basel), 2023 Zhu Y, Shang H.
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Therapeutic Monitoring of Vancomycin and Factors Affecting Survival in ICU Patients with Infections. [PDF]
Pharmaceuticals (Basel)Berdnikova NG +10 more
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