Affiliation:
1. College of Mathematics and Systems Science, Shandong University of Science and Technology , Qingdao , 266590 , P. R. China
Abstract
AbstractIn this article, we aimed to study a class of nonhomogeneous fractional (p,q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities inRN{{\mathbb{R}}}^{N}. By appealing to a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial nonnegative solutions is obtained. In particular, we also consider Choquard-type nonlinearities in the second part of this article. More precisely, with the help of Hardy-Littlewood-Sobolev inequality, we obtain the existence of nontrivial solutions for the related systems based on the same approach. Finally, we obtain the corresponding existence results for the fractional (p,q)-Laplacian systems in the case ofN=sp=lqN=sp=lq. It is worth pointing out that using fixed point argument to seek solutions for a class of nonhomogeneous fractional (p,q)-Laplacian systems is the main novelty of this article.
Reference51 articles.
1. D. Applebaum, Lévy processes-from probability to finance and quantum groups, Notes Amer. Math. Soc. 51 (2004), 1336–1347.
2. G. Autuori and P. Pucci, Elliptic problems involving the fractional Laplacian in RN, J. Differ. Equ. 255 (2013), 2340–2362.
3. L. Baldelli, Y. Brizi, and R. Filippucci, Multiplicity results for (p,q)-Laplacian equations with critical exponent in RN and negative energy, Calc. Var. Partial Differ. Equ. 60 (2021), 1–30.
4. M. Bhakta, S. Chakraborty, and P. Pucci, Fractional Hardy-Sobolev equations with nonhomogeneous terms, Adv. Nonlinear Anal. 10 (2021), 1086–1116.
5. H. Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext. Springer, New York, 2011.
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献