Description
| - We investigate the system of two nonlinear differential equations $x''+k(x,y)x=0$, $y''+l(x,y)y=0$, with nonlinearities $k(x,y)$ and $l(x,y)$. We consider the functions $k(x,y)$ and $l(x,y)$ to be constant on each quadrant of $R^{2}$, which means that $k$ and $l$ are equal to different constants $k_{1}, k_{2}, k_{3}, k_{4}$ and $l_{1}, l_{2}, l_{3}, l_{4}$, respectively, for each of four quadrants. We formulate sufficient condition on constants $k_{i}$ and $l_{j}$, $i, j\in\{1,2,3,4\}$, such that the problem has a nontrivial $T$-periodic solution.
- We investigate the system of two nonlinear differential equations $x''+k(x,y)x=0$, $y''+l(x,y)y=0$, with nonlinearities $k(x,y)$ and $l(x,y)$. We consider the functions $k(x,y)$ and $l(x,y)$ to be constant on each quadrant of $R^{2}$, which means that $k$ and $l$ are equal to different constants $k_{1}, k_{2}, k_{3}, k_{4}$ and $l_{1}, l_{2}, l_{3}, l_{4}$, respectively, for each of four quadrants. We formulate sufficient condition on constants $k_{i}$ and $l_{j}$, $i, j\in\{1,2,3,4\}$, such that the problem has a nontrivial $T$-periodic solution. (en)
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