Existence and multiplicity of positive periodic solutions to Minkowski-curvature equations without coercivity condition

2021 ◽  
pp. 125840
Author(s):  
Xingchen Yu ◽  
Shiping Lu ◽  
Fanchao Kong
Keyword(s):  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Coercivity Condition ◽  
Existence And Multiplicity

Positive periodic solutions to the forced non-autonomous Duffing equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiří Šremr
Keyword(s):  
Periodic Solutions ◽  
Positive Solutions ◽  
Periodic Problem ◽  
Duffing Equation ◽  
Positive Periodic Solutions ◽  
Duffing Equations ◽  
Existence And Multiplicity ◽  
Constant Coefficients ◽  
Multiplicity Of Positive Solutions

Abstract We study the existence and multiplicity of positive solutions to the periodic problem for a forced non-autonomous Duffing equation u ′′ = p ⁢ ( t ) ⁢ u - h ⁢ ( t ) ⁢ | u | λ ⁢ sgn ⁡ u + f ⁢ ( t ) ; u ⁢ ( 0 ) = u ⁢ ( ω ) , u ′ ⁢ ( 0 ) = u ′ ⁢ ( ω ) , u^{\prime\prime}=p(t)u-h(t)\lvert u\rvert^{\lambda}\operatorname{sgn}u+f(t);\quad u(0)=u(\omega),\ u^{\prime}(0)=u^{\prime}(\omega), where p , h , f ∈ L ⁢ ( [ 0 , ω ] ) p,h,f\in L([0,\omega]) and λ > 1 \lambda>1 . The obtained results are compared with the results known for the equations with constant coefficients.

scholarly journals On Positive Periodic Solutions to Nonlinear Fifth-Order Differential Equations with Six Parameters

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Yunhai Wang ◽  
Fanglei Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Function ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Existence And Multiplicity ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fifth Order

We study the existence and multiplicity of positive periodic solutions to the nonlinear differential equation:u5(t)+ku4(t)-βu3-ξu″(t)+αu'(t)+ωu(t)=λh(t)f(u),  in  0≤t≤1,  ui(0)=ui(1),  i=0,1,2,3,4, wherek,α,ω,λ>0,  β,ξ∈R,h∈C(R,R)is a 1-periodic function. The proof is based on the Krasnoselskii fixed point theorem.

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