论文标题
与扩散的准透明性问题的阳性径向溶液的存在和不存在
Existence and nonexistence of positive radial solutions of a quasilinear Dirichlet problem with diffusion
论文作者
论文摘要
在本文中，存在和不存在的结果是dirichlet $ m $ m $ -laplacian问题的积极径向解决方案，具有不同的权重和一个扩散术语，在形式$ \ big（a（| x |）+g（u）+g（u）\ big）^{ - γ} $中，具有$γ> 0 $ a $ a $ a $ a $ a $ a $ a $ g $ a positions natures proventions。确切地说，我们获得了一个新的临界指数$ m^*_ {α，β，γ} $，该指数扩展了一个相对的情况，没有扩散，并且它与阳性径向溶液的不存在。结果是通过多种工具获得的，例如对著名的吹气技术，liouville型定理，固定点定理和poho \ v zaev-pucci-serrin类型身份的适当修改。
In this paper existence and nonexistence results of positive radial solutions of a Dirichlet $m$-Laplacian problem with different weights and a diffusion term inside the divergence of the form $\big(a(|x|)+g(u)\big)^{-γ}$, with $γ>0$ and $a$, $g$ positive functions satisfying natural growth conditions, are proved. Precisely, we obtain a new critical exponent $m^*_{α,β,γ}$, which extends the one relative to case with no diffusion and it divides existence from nonexistence of positive radial solutions. The results are obtained via several tools such as a suitable modification of the celebrated blow up technique, Liouville type theorems, a fixed point theorem and a Poho\v zaev-Pucci-Serrin type identity.
