论文标题
不平衡的分数椭圆问题与指数非线性：亚临界和关键案例
Unbalanced fractional elliptic problems with exponential nonlinearity: subcritical and critical cases
论文作者
论文摘要
本文讨论了解决方案的定性分析 以下$（p，q）$ - 分数方程：\ begen {qore*} \ begin {array} {rllll} {rllll}（-Δ）^{s_1} _ {p} _ {p} u+（ - δ） \ big（| u |^{p-2} u+| u |^{q-2} u \ big）= k（x）\ frac {f（u）} {| x |^|^\ ba} \; \text{ in } \mb R^N, \end{array} \end{equation*} \noi where $1< q< p$, $0<s_2\leq s_1<1$, $ps_1=N$, $\ba\in[0,N)$, and $V,K:\mb R^N\to\mb R$, $f:\mb r \ to \ mb r $是满足某些自然假设的连续功能。当$ f $具有亚临界增长以及有关指数非线性的关键框架时，我们都担心案例。通过将分数Sobolev空间的Moser-trudinger类型不等式与Schwarz对称技术和相关变分方法相结合，我们证明了非负溶液的存在。
This paper deals with the qualitative analysis of solutions to the following $(p,q)$-fractional equation: \begin{equation*} \begin{array}{rllll} (-Δ)^{s_1}_{p}u+(-Δ)^{s_2}_{q}u+V(x) \big(|u|^{p-2}u+|u|^{q-2}u\big) = K(x)\frac{f(u)}{|x|^\ba} \; \text{ in } \mb R^N, \end{array} \end{equation*} \noi where $1< q< p$, $0<s_2\leq s_1<1$, $ps_1=N$, $\ba\in[0,N)$, and $V,K:\mb R^N\to\mb R$, $f:\mb R\to \mb R$ are continuous functions satisfying some natural hypotheses. We are concerned both with the case when $f$ has a subcritical growth and with the critical framework with respect to the exponential nonlinearity. By combining a Moser-Trudinger type inequality for fractional Sobolev spaces with Schwarz symmetrization techniques and related variational methods, we prove the existence of nonnegative solutions.
