非齐次Lagrange系统同宿型解的存在性
On the existence of homoclinic type solutions of inhomogenous Lagrangian systems
摘要：
研究了一类$\ddot{q}(t)-q(t)+a(t)\nabla G(q(t))=f(t)$型二阶Lagrange系统的同宿型解的存在性，其中$t\in\mathbb{R}$，$q\in\mathbb{R}^n$，$a\colon\mathbb{R}\to\mathbb{R}$是连续的有界函数，$G\colon\mathbb{R}^n\to\mathbb{R}$是满足Ambrosetti-Rabinowitz超二次增长条件的$C^1$ -光滑势，$f\colon\mathbb{R}\to\mathbb{R}^n$是连续的有界平方可积〔的〕强迫项.得到了一类二阶微分方程近似序列的$2k$ -周期解的极限同宿型解.
英文摘要：
We study the existence of homoclinic type solutions for second order Lagrangian systems of the type $\ddot{q}(t)-q(t)+a(t)\nabla G(q(t))=f(t)$, where $t\in\mathbb{R}$, $q\in\mathbb{R}^n$, $a\colon\mathbb{R}\to\mathbb{R}$ is a continuous positive bounded function, $G\colon\mathbb{R}^n\to\mathbb{R}$ is a $C^1$-smooth potential satisfying the Ambrosetti-Rabinowitz superquadratic growth condition and $f\colon\mathbb{R}\to\mathbb{R}^n$ is a continuous bounded square integrable forcing term. A homoclinic type solution is obtained as limit of $2k$-periodic solutions of an approximative sequence of second order differential equations.
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