Existence and uniqueness of solution for a singular elliptic differential equation
Shanshan Gu, Bianxia Yang, Wenrui Shao · Advances in Nonlinear Analysis · 2024
Abstract In this article, we are concerned about the existence, uniqueness, and nonexistence of the positive solution for: − Δ u − 1 2 ( x ⋅ ∇ u ) = μ h ( x ) u q − 1 + λ u − u p , x ∈ R N , u ( x ) → 0 , as ∣ x ∣ → + ∞ , \left\{\begin{array}{l}-\Delta u-\frac{1}{2}\left(x\cdot abla u)=\mu h\left(x){u}^{q-1}+\lambda u-{u}^{p},\hspace{1.0em}x\in {{\mathbb{R}}}^{N},\\ u\left(x)\to 0,\hspace{1em}\hspace{0.1em}\text{as}\hspace{0.1em}\hspace{0.33em}| x| \to +\infty ,\end{array}\right. where N ⩾ 3 N\geqslant 3 , 0 0 \lambda \gt 0 , p > 1 p\gt 1 , μ > 0