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Advanced Nonlinear Studies 5 (2005), 163–196 Periodic Solutions of Symmetric Elliptic Singular Systems Flaviano Battelli ∗ Dipartimento di Scienze Matematiche, Ingegneria Marche Politechnic University Via Brecce Bianche 1, 60131 Ancona - Italy e-mail: fbat@dipmat.univpm.it Michal Fečkan † Department of Mathematical Analysis and Numerical Mathematics Comenius University Mlynská dolina, 842 48 Bratislava - Slovakia e-mail: michal.feckan@fmph.uniba.sk Received in revised form 23 November 2004 Communicated by Kenneth Palmer Abstract We show the existence of

Advanced Nonlinear Studies 15 (2015), 241–252 Levinson’s Problem on Affine-Periodic Solutions∗ Yong Li College of Mathematics Jilin University, Changchun 130012, P.R.China. Fushan Huang† College of Mathematics Jilin University, Changchun 130012, P.R.China. e-mail: huangfushan87@163.com Received 20 May 2014 Communicated by Yiming Long Abstract In this paper, Levinson’s problem is introduced to affine-periodic systems. It is proved that every affine-dissipative-repulsive system admits an affine-periodic solution, which extends previous well-known results for

Advanced Nonlinear Studies 11 (2011), 201-220 Periodic Solutions of Systems with Singularities of Repulsive Type Pablo Amster∗ Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina and Consejo Nacional de Investigaciones Cientı́ficas y Técnicas (CONICET) e-mail: pamster@dm.uba.ar Manuel Maurette∗ Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Pabellón I, (1428) Buenos Aires

References [1] J. H. Liu, Bounded and periodic solutions of differential equations in Banach space, Appl. Math. Comput., 65(1994), 141-150. [2] J. H. Liu, Bounded and periodic solutions of semilinear evolution equations, Dynam. Syst. Appl., 4(1995), 341-350. [3] J. H. Liu, Bounded and periodic solutions of finite delay evolution equations, Nonlinear Anal.:TMA, vol. 34(1998), 101-111. [4] J. H. Liu, T. Naito, N. V. Minh, Bounded and periodic solutions of infinite delay evolution equations, J. Math. Anal. Appl., 286(2003), 705-712. [5] E. Hernández, D. O'Regan, On

Adv. Nonlinear Anal. 2015; 4 (4):251–261 Research Article Chun Li, Ravi P. Agarwal and Chun-Lei Tang* Innitely many periodic solutions for ordinary p-Laplacian systems Abstract:Someexistence theoremsare obtained for innitelymanyperiodic solutionsof ordinary p-Laplacian systems by minimax methods in critical point theory. Keywords: Periodic solutions, critical points, p-Laplacian systems MSC 2010: 34C25, 35B38, 47J30 DOI: 10.1515/anona-2014-0048 Received October 24, 2014; revised March 6, 2015; accepted June 26, 2015 1 Introduction and main results Consider the p

1 Introduction It is well known that soliton equations have very wide applications in fields of fluid dynamics, plasma physics, optical fibers, biology, and many more. Quasi-periodic solutions of soliton equations are of great importance for it reveals inherent structure of solutions and describes quasi-periodic actions of nonlinear phenomenon, especially can be used to find multi-soliton solutions and elliptic function solutions, and similar ones to these. Since the first research on finite-gap solutions of Korteweg–de Vries equation around 1975, there has been

Periodic Solutions of Asymptotically Linear Hamiltonian Systems without Twist Conditions Rong Chenga,b and Dongfeng Zhangb a College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China b Department of Mathematics, Southeast University, Nanjing 210096, China Reprint requests to R. C.; E-mail: mathchr@163.com Z. Naturforsch. 65a, 445 – 452 (2010); received April 6, 2009 / revised September 15, 2009 In dynamical system theory, especially in many fields of applications from mechanics, Hamilto- nian systems play

forward) finite-dimensional Hamiltonian systems (FDHSs) will be utilised for getting quasi-periodic solutions of the mKN hierarchy, which are the compound integrable systems of the positive-order Kaup-Newell (pKN) hierarchy labelled by the following KN equations [ 28 ]: (1) { q ˜ t 2 = 1 2 q ˜ x x − q ˜ q ˜ x r ˜ − 1 2 q ˜ 2 r ˜ x , r ˜ t 2 = − 1 2 r ˜ x x − 1 2 q ˜ x r ˜ 2 − q ˜ r ˜ r ˜ x , $$\left\{ {\matrix{ {{{\tilde q}_{{t_2}}} = {1 \over 2}{{\tilde q}_{xx}} - \tilde q{{\tilde q}_x}\tilde r - {1 \over 2}{{\tilde q}^2}{{\tilde r}_x},} \cr {{{\tilde r}_{{t_2

Advanced Nonlinear Studies 2 (2002), 299-312 Periodic Solutions of Singular Nonlinear Perturbations of the Ordinary p-Laplacian P. Jebelean Department of Mathematics, West University of Timigoara Bv. V. PCrvan, No. 4, 1900 Timigoara, Romania e-mail: jebelean@hilbert.math.uvt.ro J. Mawhin Department of Mathematics, UniversitC Catholique de Louvain ch. du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium e-mail: mawhin@math.ucl.ac.be Received 14 May 2002 Dedicated to George Dinca for his sixtieth birthday anniversary Abstract Using some recent extensions

Advanced Nonlinear Studies 6 (2006), 109 – 132 Periodic Solutions of Symmetric Elliptic Singular Systems: the Higher Codimension Case Flaviano Battelli ∗ Dipartimento di Scienze Matematiche, Ingegneria Marche Politechnic University Via Brecce Bianche 1, 60131 Ancona - Italy e-mail: fbat@dipmat.univpm.it Michal Fečkan† Department of Mathematical Analysis and Numerical Mathematics Comenius University Mlynská dolina, 842 48 Bratislava - Slovakia and Mathematical Institute of the Slovak Academy of Sciences Štefánikova 49, 814 73 Bratislava, Slovakia e