论文标题
$ \ mathbb {r}^n $中的半连接椭圆问题：潜力和非线性术语之间的相互作用
Semilinear elliptic problems in $\mathbb{R}^N$: the interplay between the potential and the nonlinear term
论文作者
论文摘要
它被认为是$ \ mathbb {r}^n $中的半连接椭圆偏微分方程，其潜力可能在无穷大时消失，并且具有亚临界增长的非线性术语。事实证明，一个积极的解决方案存在取决于无穷大势的衰减与原点非线性项的行为之间的相互作用。证明基于惩罚论点，变分方法和$ l^\ infty $估计。这些估计值允许处理非线性源可能在起源附近具有超临界，批判或亚临界行为的设置。当非线性项是奇数时，提供了多个和无限多个解决方案的结果。
It is considered a semilinear elliptic partial differential equation in $\mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the interplay between the decay of the potential at infinity and the behavior of the nonlinear term at the origin. The proof is based on a penalization argument, variational methods, and $L^\infty$ estimates. Those estimates allow dealing with settings where the nonlinear source may have supercritical, critical, or subcritical behavior near the origin. Results that provide the existence of multiple and infinitely many solutions when the nonlinear term is odd are also established.
