Monotone and Oscillatory Solutions of a Class of Nonlinear Differential Equations
Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions
The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.
Monotone methods applied to some higher order boundary value problems.
Monotone Methods for Periodic solutions of Second Order Scalar Functional Differential Equations.
Monotone solutions of a nonautonomous differential equation for a sedimenting sphere.
Monotone trajectories of dynamical systems and Clarke's generalized Jacobian.
Monotonic properties of zeros and extremants of the differential equation
Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems
We first examine conditions implying monotonicity of the period function for potential systems with a center at 0 (in the whole period annulus). We also present a short comparative survey of the different criteria. We apply these results to quadratic Loud systems for various values of the parameters D and F. In the case of noncritical periods we propose an algorithm to test the monotonicity of the period function for . Our results may be viewed as a contribution to proving (or disproving) a conjecture...
Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems
We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function...
Monotonicity of the period map of a non-Hamiltonian center.
Monotonicity properties of oscillatory solutions of differential equation
We obtain monotonicity results concerning the oscillatory solutions of the differential equation . The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.
Monotonicity properties of the linear combination of derivatives of some special functions
Monotonicity theorems concerning differential equations
Monotonicity theorems for second order non-linear differential equations
More on oscillation of th-order equations.
Morse theory and existence of periodic solutions of convex hamiltonian systems
Motion of spirals by crystalline curvature
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Multibump solutions for a class of lagrangian systems slowly oscillating at infinity
Multibump solutions for an almost periodically forced singular Hamiltonian system.