Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equationsReportar como inadecuado



 Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations


Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Descargar gratis o leer online en formato PDF el libro: Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations
By introducing a suitable setting, we study the behavior of finite Morse index solutions of the equation \ -\{div} (|x|^\theta abla v)=|x|^l |v|^{p-1}v \;\;\; \{in $\Omega \subset \R^N \; (N \geq 2)$}, \leqno(1) \ where $p>1$, $\theta, l\in\R^1$ with $N+\theta>2$, $l-\theta>-2$, and $\Omega$ is a bounded or unbounded domain. Through a suitable transformation of the form $v(x)=|x|^\sigma u(x)$, equation (1) can be rewritten as a nonlinear Schr\-odinger equation with Hardy potential $$-\Delta u=|x|^\alpha |u|^{p-1}u+\frac{\ell}{|x|^2} u \;\; \{in $\Omega \subset \R^N \;\; (N \geq 2)$}, \leqno{(2)}$$ where $p>1$, $\alpha \in (-\infty, \infty)$ and $\ell \in (-\infty,(N-2)^2-4)$. We show that under our chosen setting for the finite Morse index theory of (1), the stability of a solution to (1) is unchanged under various natural transformations. This enables us to reveal two critical values of the exponent $p$ in (1) that divide the behavior of finite Morse index solutions of (1), which in turn yields two critical powers for (2) through the transformation. The latter appear difficult to obtain by working directly with (2).



Autor: Yihong Du; Zongming Guo

Fuente: https://archive.org/







Documentos relacionados