### Exponential stability of two coupled second-order evolution equations.

Wan, Qian, Xiao, Ti-Jun (2011)

Advances in Difference Equations [electronic only]

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Wan, Qian, Xiao, Ti-Jun (2011)

Advances in Difference Equations [electronic only]

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Peng Chen, Xianhua Tang (2014)

Applications of Mathematics

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The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system $$\begin{array}{c}\frac{\mathrm{d}}{\mathrm{d}t}\left(\right|\dot{u}\left(t\right){|}^{p-2}\dot{u}\left(t\right))=\nabla F(t,u\left(t\right)),\phantom{\rule{1.0em}{0ex}}\text{a.e.}\phantom{\rule{4pt}{0ex}}t\in [0,T],\\ u\left(0\right)-u\left(T\right)=\dot{u}\left(0\right)-\dot{u}\left(T\right)=0,\\ \Delta {\dot{u}}^{i}\left({t}_{j}\right)={\dot{u}}^{i}\left({t}_{j}^{+}\right)-{\dot{u}}^{i}\left({t}_{j}^{-}\right)={I}_{ij}\left({u}^{i}\left({t}_{j}\right)\right),\phantom{\rule{4pt}{0ex}}i=1,2,\cdots ,N;\phantom{\rule{4pt}{0ex}}j=1,2,\cdots ,m.\end{array}$$ By using the least action principle and the saddle point theorem, some new existence theorems are obtained for second-order $p$-Laplacian systems with or without impulse under weak sublinear growth conditions, improving some existing results in the literature.

Donal O'Regan (1998)

Czechoslovak Mathematical Journal

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Existence results are established for the resonant problem ${y}^{\text{'}\text{'}}+{\lambda}_{m}\phantom{\rule{0.166667em}{0ex}}a\phantom{\rule{0.166667em}{0ex}}y=f(t,y)$ a.e. on $[0,1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a\in {L}_{\mathrm{l}oc}^{1}(0,1)$ with $a>0$ a.e. on $[0,1]$ and ${\int}_{0}^{1}x(1-x)a\left(x\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x<\infty $.

Panigrahi, S. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Aglić Aljinović, A., Pečarić, J., Vukelić, A. (2005)

Journal of Inequalities and Applications [electronic only]

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Dragomir, S.S. (2008)

Journal of Inequalities and Applications [electronic only]

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Kharibegashvili, S. (2005)

Boundary Value Problems [electronic only]

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M.K. Potapov, B.V. Simonov, B. Lakovich (1995)

Publications de l'Institut Mathématique

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Bougoffa, Lazhar (2004)

Applied Mathematics E-Notes [electronic only]

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