Existence of periodic solutions for p-Laplacian equation under the frame of Fu % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmqr1ngBPrgitL % xBI9gBaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8srps0lbb % f9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYx % ir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGaca % GaaeqabaWaaqaafaaakeaaieaacuWFJbWygaafaaaa!3F1A! $$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{c} $$ ik spectrum

2011 ◽  
Vol 27 (3) ◽  
pp. 545-554 ◽  
Author(s):  
Wen Bin Liu ◽  
Yong Li
Keyword(s):  
Periodic Solutions ◽  
Laplacian Equation ◽  
Existence Of Periodic Solutions

scholarly journals On the Study Of Asymptotically Almost Periodic Solutions of a Class of Impulsive Population Models

2018 ◽  
Vol 36 (3) ◽  
pp. 597-601
Author(s):  
Li Wang
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Population Models ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Laplacian Equation ◽  
Existence Of Periodic Solutions ◽  
Functional Differential ◽  
Solutions Of Equations ◽  
Asymptotically Almost Periodic

Based on the Mawhin continuous theorem, the existence of strictly positive asymptotically almost periodic solutions of a class of impulsive population models is studied. The conclusion generalizes the conclusion of the existing literatures. Since the Mawhin continuous theorem is only used to prove the existence of periodic solutions or almost periodic solutions of equations (for example:impulsive differential equation, functional differential equation, integral equation, Lienard equation, P-Laplacian equation), the main result is innovative.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

2020 ◽  
Vol 20 (3) ◽  
pp. 725-737 ◽  
Author(s):  
Zhenping Feng ◽  
Zhuoran Du
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Smooth Function ◽  
Fractional Laplacian ◽  
Type Inequality ◽  
Energy Functional ◽  
Large Integer ◽  
Existence Of Periodic Solutions ◽  
Double Well Potential

AbstractWe consider periodic solutions of the following problem associated with the fractional Laplacian: {(-\partial_{xx})^{s}u(x)+\partial_{u}F(x,u(x))=0} in {\mathbb{R}}. The smooth function {F(x,u)} is periodic about x and is a double-well potential with respect to u with wells at {+1} and -1 for any {x\in\mathbb{R}}. We prove the existence of periodic solutions whose periods are large integer multiples of the period of F about the variable x by using variational methods. An estimate of the energy functional, Hamiltonian identity and Modica-type inequality for periodic solutions are also established.

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