论文标题
存在涉及区域分数laplacian的椭圆方程的解决方案（0，\ frac12] $
Existence of solutions to elliptic equations involving regional fractional Laplacian with order $(0,\frac12]$
论文作者
论文摘要
我们本文的目的是通过区域分数laplacian $$调查椭圆方程的积极解决方案 （ - δ）_ {b_1}^s u +u = h（x，u）\ quad {\ rm in} \ \，b_1，\ qquad u \ in C_0（B_1）， $$ 其中$（δ）_ {b_1}^s $带有$ s \ in（0，\ frac12] $是区域分数laplacian，而$ h $是非线性。 通常，预计在（0，\ frac12] $ in（0，\ frac12] $）的区域分数拉普拉斯的方程中，未预计在边界处消失的阳性解决方案。 $ h（x，t）= f（x）$或$ h（x，t）= h_1（x）\，t^p+εh_2（x）$，其中$ p> 1 $，$ε> 0 $ small和$ f，h_1，h_1，h_2 $在适当的条件下是持续的，rady和降低的条件。
Our purpose of this paper is to investigate positive solutions of the elliptic equation with regional fractional Laplacian $$ ( - Δ)_{B_1}^s u +u= h(x,u) \quad {\rm in} \ \, B_1,\qquad u\in C_0(B_1), $$ where $( - Δ)_{B_1}^s$ with $s\in(0,\frac12]$ is the regional fractional Laplacian and $h$ is the nonlinearity. Ordinarily, positive solutions vanishing at the boundary are not anticipated to be derived for the equations with regional fractional Laplacian of order $s\in(0,\frac12]$. Positive solutions are obtained when the nonlinearity assumes the following two models: $h(x,t)=f(x)$ or $h(x,t)=h_1(x)\, t^p+ εh_2(x)$, where $p>1$, $ε>0$ small and $f, h_1, h_2$ are Hölder continuous, radially symmetric and decreasing functions under suitable conditions.
