Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities

2001 ◽  
Vol 43 (2) ◽  
pp. 233-251 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Mark McKibben ◽  
Simeon Reich
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Discontinuous Nonlinearities

scholarly journals Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 792-805
Author(s):  
Junfei Cao ◽  
Zaitang Huang
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Initial Conditions ◽  
Asymptotically Periodic ◽  
Semilinear Evolution Equations ◽  
Asymptotically Periodic Solutions

AbstractIn this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.

Jacobi Elliptic Function Rational Expansion Method with Symbolic Computation to Construct New Doubly-periodic Solutions of Nonlinear Evolution Equations

2004 ◽  
Vol 59 (9) ◽  
pp. 529-536 ◽  
Author(s):  
Yong Chen ◽  
Qi Wang ◽  
Biao Lic
Keyword(s):  
Periodic Solutions ◽  
Symbolic Computation ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Rational Form

A new Jacobi elliptic function rational expansion method is presented by means of a new general ansatz and is very powerful, with aid of symbolic computation, to uniformly construct more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations (NLEEs). We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we obtain the solutions found by most existing Jacobi elliptic function expansion methods and find other new and more general solutions at the same time. When the modulus of the Jacobi elliptic functions m→1 or 0, the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions are also found.

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