Results 161 to 170 of about 1,158 (197)
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Journal of Mathematical Physics, 2005
We consider a perturbation of the Fitzhugh–Nagumo equation. The perturbation is proportional to the electric potential across the cell membrane. The purpose of this investigation is to determine the effects of a change in electric potential across the cell membrane.
Shih, M., Momoniat, E., Mahomed, F. M.
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We consider a perturbation of the Fitzhugh–Nagumo equation. The perturbation is proportional to the electric potential across the cell membrane. The purpose of this investigation is to determine the effects of a change in electric potential across the cell membrane.
Shih, M., Momoniat, E., Mahomed, F. M.
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Dynamic boundary value problems of the second-order: Bernstein–Nagumo conditions and solvability
Nonlinear Analysis: Theory, Methods & Applications, 2007The existence of solutions to the dynamic boundary value problem \[ y^{\triangle\triangle}=f(t,y^\sigma,y^\triangle),\quad t\in[a,b]_T,\quad y(a)=A,\quad y(\sigma^2(b))=B, \] is studied. Here, \(T\) is the so-called ``time scale'' (in this paper \(T\equiv \mathbb{R}\) or all points in \(T\) are isolated), \([a,b]_T=\{t\in T:\;a\leq t\leq b\},\) \(f:[a ...
Henderson, Johnny +1 more
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Nagumo type condition for partial differential inclusions
Nonlinear Analysis: Theory, Methods & Applications, 1988The viability problem for autonomous differential inclusions in Hilbert and Banach spaces and for the generalized equation \(0\in F(x)\) is studied. Let V, H be two Hilbert spaces such that \(V\subset H=H'\subset V'\), the inclusions being compact and dense, and let \(K\subset H\) be a closed set with the so-called internal approximation property.
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Existence and regularity for the Fitzhugh-Nagumo equations with inhomogeneous boundary conditions
Nonlinear Analysis: Theory, Methods & Applications, 1990The author considers the FitzHugh-Nagumo equations which model the transmission of electrical impulses in a nerve axon. Existence and uniqueness of solutions to an initial-boundary value problem with irregular data is proved by the use of a Galerkin method.
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Journal of Applied Mathematics and Computing, 2007
The authors study the \(p\)-Laplacian equation \[ (\phi_p(u'))'=f(t,u,u'),\quad t\in (0,1), \] with the three-point boundary conditions \[ u'(0)=0,\quad u(1)=u(\eta),\quad \eta\in(0,1). \] The solvability of the boundary value problem at resonance is discussed by the method of two pairs of lower and upper solutions.
Zhang, Jianjun +3 more
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The authors study the \(p\)-Laplacian equation \[ (\phi_p(u'))'=f(t,u,u'),\quad t\in (0,1), \] with the three-point boundary conditions \[ u'(0)=0,\quad u(1)=u(\eta),\quad \eta\in(0,1). \] The solvability of the boundary value problem at resonance is discussed by the method of two pairs of lower and upper solutions.
Zhang, Jianjun +3 more
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Nagumo and Landesman-Lazer type conditions for nonlinear second order systems
Nonlinear Differential Equations and Applications NoDEA, 2007We study the existence of solutions for a nonlinear second order system of ordinary differential equations under various boundary conditions. Assuming suitable Nagumo type conditions we prove the existence of at least one solution applying the method of upper and lower solutions.
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Moscow University Computational Mathematics and Cybernetics, 2011
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Efficient numerical method for the Fitzhugh-Nagumo equations with Neumann boundary conditions
SCIREA Journal of Physics, 2023Hao Zhou +3 more
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Higher order nonlinear two-point boundary value problems with sign-type Nagumo condition
2012In this paper we present existence and location results for two-point boundary value problems for third and fourth order fully nonlinear differential equations. Nonlinearities are assumed to satisfy a sign-type Nagumo condition which allows an asymmetric unbounded behavior The arguments make use of lower and upper solutions method and degree theory.
Santos, Ana Isabel +2 more
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NAGUMO CONDITIONS FOR ORDINARY DIFFERENTIAL EQUATIONS
1975Joan E. Innes, Lloyd K. Jackson
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