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Periodic solutions for SDEs through upper and lower solutions
Discrete & Continuous Dynamical Systems - B, 2020 We study a kind of better recurrence than Kolmogorov's one: periodicity recurrence,which corresponds periodic solutions in distribution for stochastic differential equations. On the basis of technique of upper and lower solutions and comparison principle, we obtain the existence of periodic solutions in distribution for stochastic differential ...
Ji, Chunyan, Xue, Yang, Li, Yong
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Almost periodic upper and lower solutions
Journal of Differential Equations, 2003 Consider the second-order equation \((*) \;\ddot{u} = f(t,u,\dot{u}),\) where \(f\) is continuous and \(T\)-periodic in \(t\). If \(f\) satisfies a Nagumo condition, then the method of upper and lower solutions is a powerful tool to establish the existence of \(T\)-periodic solutions of \((*)\).
R. Ortega, M.E. Tarallo
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Upper and Lower Solutions with “Jumps”
Journal of Mathematical Analysis and Applications, 1998 Consider the periodic boundary value problem \((*)\) \(dx/dt = f(t,x)\), \(x(0)=x(T)\) where \(f:[0,T] \times \mathbb{R} \rightarrow \mathbb{R}\) is a Carathéodory function. The authors introduce the concept of piecewise absolutely continuous lower and upper solutions to \((*)\) (which can have jumps) and prove that the existence of ordered piecewise ...
Liz, Eduardo, Pouso, Rodrigo L
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On the stability of solutions of the Lichnerowicz-York equation [PDF]
, 2013 We study the stability of solution branches for the Lichnerowicz-York equation at moment of time symmetry with constant unscaled energy density. We prove that the weak-field lower branch of solutions is stable whilst the upper branch of strong-field ...
Walsh, Darragh M
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Singular Problems: An Upper and Lower Solution Approach
Journal of Mathematical Analysis and Applications, 2000 Consider the problem \[ (py')'+p(t)q(t)f(t,y)=0, \quad \lim_{t\to 0+}p(t)y'(t)=0,\;y(1)=0, \tag{1} \] where \(p\) can be zero at both end points \(0\) and \(1\), \(q\) can be singular at these points and \(f\in{\mathcal C}([0,1]\times (0,\infty))\) can have a singularity at \(y=0\). The authors assume the existence of a sequence of constants \(\rho_n\)
O'Regan, D., Agarwal, R.P.
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Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow [PDF]
, 2010 The appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail.
B. ECKHARDT +6 more
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A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient [PDF]
, 2006 The existence of a mean-square continuous strong solution is established for vector-valued Itö stochastic differential equations with a discontinuous drift coefficient, which is an increasing function, and with a Lipschitz continuous diffusion ...
Halidias, Nikolaos, Kloeden, Peter E.
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Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries [PDF]
, 2018 In this work we study the behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating thin region with reaction terms concentrated in a neighborhood of the ...
Arrieta, José M. +2 more
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Lower and Upper Solutions for Even Order Boundary Value Problems [PDF]
Mathematics, 2019 In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions of a considered problem could imply the existence of solution of another one with different boundary ...
Alberto Cabada, Lucía López-Somoza
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, 2011 We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the unknown ...
Figueroa, Rubén, Pouso, Rodrigo López
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