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Related papers: The Ambrosetti-Prodi periodic problem: Different r…

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We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation,…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 Fred Cooper , Avinash Khare , Uday Sukhatme

This paper aims to provide a Melnikov-like function that governs the existence of periodic solutions bifurcating from period annuli in certain families of second-order discontinuous differential equations of the form $\ddot{x}+\alpha\;…

Dynamical Systems · Mathematics 2024-08-23 Douglas D. Novaes , Luan V. M. F. Silva

In this paper we study results of existence and non-existence of solutions for the following Ambrosetti-Prodi type problem $$ \left\{ \begin{array}{lcl} -\Delta u=P(x)\Big( g(u)+f(x)\Big) \mbox{ in } \mathbb{R}^N,\\ u \in D^{1,2}(\R^N),\…

Analysis of PDEs · Mathematics 2020-06-04 Claudianor O. Alves , Romildo N. de Lima , Alânnio B. Nóbrega

The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…

Dynamical Systems · Mathematics 2013-06-20 Benjamin Ricaud

We prove the existence of at least two geometrically different periodic solution with winding number N for the forced relativistic pendulum. The instability of a solution is also proved. The proof is topological and based on the version of…

Dynamical Systems · Mathematics 2020-04-22 Stefano Marò

We study the dynamics of the positive solutions of a second-order, Ricker-type exponential difference equation with periodic parameters. We find that qualitatively different dynamics occur depending on whether the period p of the main…

Dynamical Systems · Mathematics 2017-02-14 N. Lazaryan , H. Sedaghat

As a consequence of the main result of this paper efficient conditions guaranteeing the existence of a $T-$periodic solution to the second order differential equation \begin{equation*} u"=\frac{h(t)}{u^{\lambda}} \end{equation*} are…

Dynamical Systems · Mathematics 2017-07-17 Manuel Zamora , José Godoy

We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the the pseudo-index…

Analysis of PDEs · Mathematics 2018-09-06 Vincenzo Ambrosio , Giovanni Molica Bisci

We study the periodic boundary value problem associated with the second order nonlinear equation \begin{equation*} u'' + ( \lambda a^{+}(t) - \mu a^{-}(t) ) g(u) = 0, \end{equation*} where $g(u)$ has superlinear growth at zero and sublinear…

Classical Analysis and ODEs · Mathematics 2015-12-23 Alberto Boscaggin , Guglielmo Feltrin , Fabio Zanolin

We prove the existence of at least one T-periodic solution (T > 0) for differential equations of the form (u'(t)/sqrt{1-u'^2(t)})'=f(u(t))+h(t), in (0,T), where f is a continuous function defined on R that satisfies a strong resonance…

Analysis of PDEs · Mathematics 2011-12-15 Laura Gonella

A system of nonlinear ordinary differential equations with forcing function is developed to model evolution processes in complex systems. In this system R, C, and P are the resource, consumption, and production functions correspondingly. F…

Atmospheric and Oceanic Physics · Physics 2017-11-01 Lev A Maslov

The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result…

Analysis of PDEs · Mathematics 2016-12-28 Vincenzo Ambrosio , Giovanni Molica Bisci

In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized Differential-Algebraic Equations with non-autonomous constraints of a particular type. We provide simple, degree theoretic…

Classical Analysis and ODEs · Mathematics 2013-11-22 Luca Bisconti , Alessandro Calamai , Marco Spadini

The aim of this note is to set in the field of dynamical systems a recent theorem by Obersnel and Omari about the presence of periodic solutions of all periods for a class of scalar time-periodic first order differential equations without…

Dynamical Systems · Mathematics 2009-11-10 Marina Pireddu

We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$. The main conditions are stated in terms of the spectrum…

Analysis of PDEs · Mathematics 2018-07-12 Vu Trong Luong , Nguyen Van Minh

By using variational methods we investigate the existence of T-periodic solutions to [(-Delta_x + m^2)^s -m^(2s)]u= f(x,u) in (0,T)^N u(x+Te_i)=u(x) for all x in R^N, i=1,...,N where s in (0,1), N>2s, T>0, m>=0 and f(x,u) is a continuous…

Analysis of PDEs · Mathematics 2018-02-20 Vincenzo Ambrosio

This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…

Classical Analysis and ODEs · Mathematics 2016-10-25 Faouzi Haddouchi , Slimane Benaicha

In this paper we study the dynamical behaviour of the differential equation \begin{equation*} x''+ax^+ -bx^-=f(t), \end{equation*} where $x^+=\max\{x,0\}$,\ $x^-=\max\{-x,0\}$, $a$ and $b$ are two different positive constants, $f(t)$ is a…

Dynamical Systems · Mathematics 2017-05-26 Peng Huang , Xiong Li , Bin Liu

It is well-known that the classical hyperbolic Kirchhoff equation admits infinitely many simple modes, namely time-periodic solutions with only one Fourier component in the space variables. In this paper we assume that, for a suitable…

Analysis of PDEs · Mathematics 2022-11-15 Marina Ghisi , Massimo Gobbino

In this paper we investigate the existence and uniqueness of bounded, periodic and almost periodic solutions for second order differential equations involving reflection of the argument.The relationship between frequency modules of forced…

Classical Analysis and ODEs · Mathematics 2013-02-05 Daxiong Piao , Na Xin