### On the asymptotic behavior of solutions of nonlinear ordinary differential equations

Kusano, Takaŝi

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Kusano, Takaŝi

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

Publications de l'Institut Mathématique

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Donal O'Regan (1995)

Commentationes Mathematicae Universitatis Carolinae

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New existence results are presented for the two point singular “resonant” boundary value problem $\frac{1}{p}{\left(p{y}^{\text{'}}\right)}^{\text{'}}+ry+{\lambda}_{m}qy=f(t,y,p{y}^{\text{'}})$ a.eȯn $[0,1]$ with $y$ satisfying Sturm Liouville or Periodic boundary conditions. Here ${\lambda}_{m}$ is the ${(m+1)}^{st}$ eigenvalue of $\frac{1}{pq}[{\left(p{u}^{\text{'}}\right)}^{\text{'}}+rpu]+\lambda u=0$ a.eȯn $[0,1]$ with $u$ satisfying Sturm Liouville or Periodic boundary data.

Bougoffa, Lazhar (2004)

Applied Mathematics E-Notes [electronic only]

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Alexander J. Zaslavski (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study a variational problem which was introduced by Hannon, Marcus and Mizel [ (2003) 145–149] to describe step-terraces on surfaces of so-called “unorthodox” crystals. We show that there is no nondegenerate intervals on which the absolute value of a minimizer is $\pi /2$ identically.

Xingyong Zhang, Yinggao Zhou (2010)

Applications of Mathematics

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The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system $$\left\{\begin{array}{c}\ddot{u}\left(t\right)=\nabla F(t,u\left(t\right)),\phantom{\rule{5.0pt}{0ex}}\text{a.e.}\phantom{\rule{4pt}{0ex}}t\in [0,T],\hfill \\ u\left(0\right)-u\left(T\right)=\dot{u}\left(0\right)-\dot{u}\left(T\right)=0.\hfill \end{array}\right.$$ Some new existence theorems are obtained by the least action principle.

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

Journal of Inequalities and Applications [electronic only]

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