论文标题
具有异质非负重的平面系统中的丰富动力学
Rich dynamics in planar systems with heterogeneous nonnegative weights
论文作者
论文摘要
本文研究了与准线性方程相关的广义sturm-liouville边界价值问题$$ - （ϕ（u'））'=λu + a（t）g（t）g（u），\ quadλ\在{\ mathb r}，$ a（$ a a）中，$ a（t）与deg分离的一个$ a（t），其中$ a \ equiv 0 $。当$ ϕ（s）= s $时，此方程包括回到Moore and Nehari，1959年的经典模型的广义原型。这是第一个在$ a \ gneq 0 $时已解决$ MATHBB {r} $的一般情况。 López-Gómez和Rabinowitz最近对带有$ a \ lneq 0 $的半线性案例进行了处理。
This paper studies the global structure of the set of nodal solutions of a generalized Sturm--Liouville boundary value problem associated to the quasilinear equation $$ -(ϕ(u'))'= λu + a(t)g(u), \quad λ\in {\mathbb R}, $$ where $a(t)$ is non-negative with some positive humps separated away by intervals of degeneracy where $a\equiv 0$. When $ϕ(s)=s$ this equation includes a generalized prototype of a classical model going back to Moore and Nehari, 1959. This is the first paper where the general case when $λ\in\mathbb{R}$ has been addressed when $a\gneq 0$. The semilinear case with $a\lneq 0$ has been recently treated by López-Gómez and Rabinowitz.
