Periodic solutions of singular equations

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August undefined, 2024

WebApr 13, 2024 · Based on the continuation theorem of coincidence degree theory and the method of upper and lower solutions, the multiple periodic solutions of the singular Rayleigh equations can be determined under the weak conditions of the term g. We discuss both the repulsive singular case and the attractive singular case. WebAug 28, 2024 · This paper is devoted to an investigation of the existence of a positive periodic solution for the following singular Liénard equation: x''+f\bigl (x (t)\bigr)x' (t)+a (t)x= \frac {b (t)} {x^ {\alpha }}+e (t), where the external force e (t) may change sign, α is a constant and \alpha >0.

Periodic solutions of singular second order differential …

WebOscillations of mechanical devices are commonly modeled with Liénard equations. Examples of such devices are MEMS (Micro-Electro-Mechanical Systems), and in … WebNov 20, 2024 · We study a second-order ordinary differential equation coming from the Kepler problem on S 2. The forcing term under consideration is a piecewise constant with … the time to do right is always right

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WebTopics typically include stable and center manifolds theorem, linearization of vector fields, variational equations, Floquet theory and Poincare; maps for periodic orbits, bifurcation of … WebSINGULAR SOLUTIONS OF ELLIPTIC EQUATIONS 15 21. F. Pacard, Solutions de ∆u = −λeu ayant des singularit´es ponctuelles prescrites, C. R. Acad. Sci. Paris S´er. I Math. 311(6)(1990), 317–320. Institute of Mathematics Simion … Web3 Solution to Problem “A” by Separation of Variables 5 4 Solving Problem “B” by Separation of Variables 7 5 Euler’s Diﬀerential Equation 8 6 Power Series Solutions 9 7 The Method of Frobenius 11 8 Ordinary Points and Singular Points 13 9 Solving Problem “B” by Separation of Variables, continued 17 10 Orthogonality 21 the time to change

Second-Order Differential Equation with Indefinite and ... - Springer

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WebThe literature on the subject of periodic solutions is enormous, and we will restrict ourselves to describing and presenting a sequence of famous examples. Let x ˙ = f ( x, t) = f ( x, t + T) be a vector differential equation with periodic forcing function f. Any its periodic solution with period T is called harmonic vibration or oscillation. WebDec 20, 2024 · In this paper, we look for positive T-periodic solutions of the first-order singular problem \begin {aligned} x' (t)=-\dfrac {1} { (x (t))^\alpha }+e (t) \end {aligned} … setting up a business nameWebDec 1, 2011 · In this paper, we are concerned with the periodic problem (1.1) u ″ ( t) + f ( u ( t)) u ′ ( t) + g ( u ( t)) = h ( t, u ( t)) for a.e. t ∈ [ 0, ω], (1.2) u ( 0) = u ( ω), u ′ ( 0) = u ′ ( ω), … the time to do what is right is always right

"WebJul 13, 2024 · Liénard equation, Mawhin's continuation theorem, periodic solution, singularity Abstract In this paper, the existence of positive periodic solutions is studied for a singular Liénard equation where the weight function has an indefinite sign. " - Periodic solutions of singular equations

Periodic solutions of singular equations

WebThis paper is a sequel to [1] where the existence of homoclinic solutions was proved for a family of singular Hamiltonian systems which were subjected to almost periodic forcing. … WebApr 11, 2024 · In what follows, we discuss the periodic solutions with three cases: \rho _1>\rho _2, \rho _1<\rho _2 and \rho _1=\rho _2. Theorem 3.1 Assume that condition ( A) and \rho _1>\rho _2 hold. Moreover, suppose there exist constants R and r satisfying R>r>0 (where R is a sufficiently large constant) such that: (H_1):

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WebDec 1, 2015 · Periodic solutions of singular equations Authors: Antonio J. Ureña University of Granada Abstract We study second-order ordinary differential equations of Newtonian … WebApr 11, 2024 · Kink wave and traveling wave solutions to the sG equation are built using the Hirota bilinear approach . Recent developments include the construction of solutions for the precise traveling wave such as single and multi-solitons, periodic waves, breaking kink waves, singular waves, periodic singular waves, and compacton wave’s solutions .

WebJan 15, 2024 · On periodic solutions of second-order differential equations with attractive-repulsive singularities. J. Differ. Equ. 248 ( 2010 ), 111 – 126. CrossRef Google Scholar 10 Hakl, R. and Zamora, M.. Periodic solutions of an indefinite singular equation arising from the Kepler's problem on the sphere. WebMar 1, 2016 · Periodic solutions of singular equations A. J. Ureña Published 1 March 2016 Mathematics Topological Methods in Nonlinear Analysis We study second-order ordinary differential equations of Newtonian type. The forcing terms under consideration are the …

WebAug 17, 2014 · In some suitable weak singularities, the existence of periodic solutions may help. 1. Introduction The theory of second-order periodic differential equation has been widely studied [1–20] because of great practical importance. In addition, may take some negative values. WebSep 11, 2024 · Essentially any second order linear equation of the form can be written as after multiplying by a proper factor. Example : Sturm-Liouville Problem Put the following equation into the form : Multiply both sides by to obtain The Bessel equation turns up for example in the solution of the two-dimensional wave equation.

WebApr 11, 2024 · Abstract. In this paper, we aim to study a second-order differential equation with indefinite and repulsive singularities. It is the first time to study differential equation …

WebDec 20, 2024 · Some efficient conditions guaranteeing the existence of periodic solutions with minimal period mT are established. These periodic solutions rotate exactly once around the singularity in the... the time to failure under creep conditionWebFeb 21, 2024 · 1. 2. In this article, some sufficient conditions for the existence of positive periodic solutions of a more general indefinite singular differential equation are established. The results are applicable to strong singularities as well as weak singularities. Some results in literature are generalized. setting up a business paypal for twitchWebJun 3, 2016 · In this paper, the problem of existence of periodic solution is studied for p -Laplacian Liénard equations with singular at x=0 and x=+\infty. By using the topological degree theory, some new results are obtained, and an example is given to illustrate the effectiveness of our results. setting up a business in wiWebIn this article, we study a periodic boundary value problem related to valveless pumping. The valveless pumping is described by the unidirectional flow of liquid in a system. We … setting up a business in wyomingWebApr 11, 2024 · The Fourier series method was used to reduce the boundary value problem to triple series equations, then to singular integral equations with Cauchy kernel. The … setting up a business loanWebApr 11, 2024 · The Fourier series method was used to reduce the boundary value problem to triple series equations, then to singular integral equations with Cauchy kernel. The analytical solutions are in a closed form for the stress field, and the stress intensity factors and the energy release rates of the phonon and phason fields near the crack tip are ... setting up a business in wisconsinWebThe rate equations for a laser with a saturable absorber have a singular point solution whose character changes from a stable focus to an unstable one with increasing pumping rate. At this transition point a stable limit cycle can emerge. thetimetofreeamerica