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Periodic segment implies infinitely many periodic solutions [PDF]

Proceedings of the American Mathematical Society, 2007
The authors of this note show that given a periodic segment for a nonautonomous ODE with periodic coefficients (i.e. a local process) and given a sequence of associated Lefschetz numbers that is not constant, then there exist infinitely many periodic solutions in the segment. The proof is based on the Shub-Sullivan theorem, see \textit{M.
Marzantowicz, Waclaw, Wójcik, Klaudiusz
openaire   +3 more sources

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

Nonlinear Analysis, 2021
In this paper, we use the Fountain theorem under the Cerami condition to study the gauged nonlinear Schrödinger equation with a perturbation in R2. Under some appropriate conditions, we obtain the existence of infinitely many high energy solutions for ...
Jiafa Xu, Jie Liu, Donal O'Regan
doaj   +1 more source

INFINITELY MANY SOLUTIONS FOR A NONLOCAL PROBLEM

Journal of Applied Analysis & Computation, 2020
Summary: Consider a class of nonlocal problems \[ \begin{cases} -(a-b\int_{\Omega}|\nabla u|^2dx)\Delta u= f(x,u),\quad &x \in\Omega, \\ u=0, & x \in\partial\Omega, \end{cases} \] where \(a>0\), \(b>0\), \(\Omega\subset \mathbb{R}^N\) is a bounded open domain, \(f:\overline{\Omega} \times \mathbb R \longrightarrow \mathbb R\) is a Carathéodory function.
Tang, Zhiyun, Ou, Zengqi
openaire   +1 more source

Infinitely many non-radial solutions for a Choquard equation

Advances in Nonlinear Analysis, 2022
In this article, we consider the non-linear Choquard equation −Δu+V(∣x∣)u=∫R3∣u(y)∣2∣x−y∣dyuinR3,-\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){| }^{2}}{| x-y| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\
Gao Fashun, Yang Minbo
doaj   +1 more source

A sequence of positive solutions for sixth-order ordinary nonlinear differential problems

Electronic Journal of Qualitative Theory of Differential Equations, 2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Gabriele Bonanno, Roberto Livrea
doaj   +1 more source

Infinitely many periodic solutions for second order Hamiltonian systems [PDF]

, 2011
In this paper, we study the existence of infinitely many periodic solutions for second order Hamiltonian systems $\ddot{u}+\nabla_u V(t,u)=0$, where $V(t, u)$ is either asymptotically quadratic or superquadratic as $|u|\to \infty$.Comment: to appear in ...
Liu, Chungen, Zhang, Qingye
core   +1 more source

On a fractional differential equation with infinitely many solutions [PDF]

, 2012
We present a set of restrictions on the fractional differential equation $x^{(\alpha)}(t)=g(x(t))$, $t\geq0$, where $\alpha\in(0,1)$ and $g(0)=0$, that leads to the existence of an infinity of solutions starting from $x(0)=0$. The operator $x^{(\alpha)}$
Băleanu, Dumitru, Mustafa, Octavian G., O'Regan, Donal   +2 more
core   +2 more sources

Integrable subsystem of Yang--Mills dilaton theory [PDF]

, 2007
With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton.
A Wereszczyński, Adam C, Adam C, Babelon O, C Adam, J Sánchez-Guillén, Makhankov V G, Ranada A F   +7 more
core   +2 more sources

Remarks on the existence of infinitely many solutions for a $p$-Laplacian equation involving oscillatory nonlinearities

Electronic Journal of Qualitative Theory of Differential Equations, 2017
In this paper, we study the existence of infinitely many solutions for an elliptic problem with the nonlinearity having an oscillatory behavior. We propose more general assumptions on the nonlinear term which improve the results occurring in the ...
Robert Stegliński
doaj   +1 more source

Infinitely many positive solutions for a nonlocal problem with competing potentials

Boundary Value Problems, 2020
The present paper deals with a class of nonlocal problems. Under some suitable assumptions on the decay rate of the coefficients, we derive the existence of infinitely many positive solutions to the problem by applying reduction method.
Jing Yang
doaj   +1 more source