• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.225-238
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• 2019

We show the boundedness and uniform Lipschitz stability for the solutions to the functional perturbed differential system $$y^{\prime}=f(t,y)+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^t}g(s,y(s),\;T_1y(s))ds+h(t,y(t),\;T_2y(t))$$, under perturbations. We impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s)$, $T_1y(s))ds$, $h(t,y(t)$, $T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.985-999
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• 2018

This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.