论文标题
超线性不确定平面系统的周期性解决方案：拓扑度方法
Periodic solutions to superlinear indefinite planar systems: a topological degree approach
论文作者
论文摘要
We deal with a planar differential system of the form \begin{equation*} \begin{cases} \, u' = h(t,v), \\ \, v' = - λa(t) g(u), \end{cases} \end{equation*} where $h$ is $T$-periodic in the first variable and strictly increasing in the second variable, $λ>0$, $ a $是改变签名的$ t $周期重量功能，$ g $是超线性。基于巧合学理论，依赖$λ$，我们证明存在$ t $ - 周期解决方案$（u，v）$，因此$ u（t）> 0 $ in \ in \ mathbb {r} $中的所有$ t \。我们的结果概括并统一了关于巴特勒在二阶微分方程正周期性解决方案（涉及线性或$ ϕ $ -laplacian型差异操作员）上的问题上的问题的先前贡献。
We deal with a planar differential system of the form \begin{equation*} \begin{cases} \, u' = h(t,v), \\ \, v' = - λa(t) g(u), \end{cases} \end{equation*} where $h$ is $T$-periodic in the first variable and strictly increasing in the second variable, $λ>0$, $a$ is a sign-changing $T$-periodic weight function and $g$ is superlinear. Based on the coincidence degree theory, in dependence of $λ$, we prove the existence of $T$-periodic solutions $(u,v)$ such that $u(t)>0$ for all $t\in\mathbb{R}$. Our results generalize and unify previous contributions about Butler's problem on positive periodic solutions for second-order differential equations (involving linear or $ϕ$-Laplacian-type differential operators).
