Yu Duan - College of Science, Guizhou University of Engineering Science, Bijie Guizhou 551700, People's Republic of China. Xin Sun - College of Science, Guizhou University of Engineering Science, , Bijie Guizhou 551700, People's Republic of China. Hong-Ying Li - School of Mathematics and Information, China West Normal University, Nanchon, Sichuan 637002, People's Republic of China.
In this work, we are interested in considering the following nonlocal problem \[ \begin{cases} -\left(a-b\displaystyle\int_{\Omega}|\nabla u|^2dx\right)\Delta u= f(x)|u|^{p-2}u, \quad\text{in }\Omega, \\ u=0, \quad\text{on }\partial\Omega, \end{cases} \] where \(\Omega\subset\mathbb{R}^{N}~(N\geq3)\) is a bounded domain with smooth boundary \(\partial\Omega, a,b>0, 1\leq p<2^*\), \(f\in L^{\frac{2^*}{2^{*}-p}}(\Omega)\) is nonzero and nonnegative. By using the variational method, some existence and multiplicity results are obtained.
Yu Duan, Xin Sun, Hong-Ying Li, Existence and multiplicity of positive solutions for a nonlocal problem, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 6056--6061
Duan Yu, Sun Xin, Li Hong-Ying, Existence and multiplicity of positive solutions for a nonlocal problem. J. Nonlinear Sci. Appl. (2017); 10(11):6056--6061
Duan, Yu, Sun, Xin, Li, Hong-Ying. "Existence and multiplicity of positive solutions for a nonlocal problem." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 6056--6061
