Affiliation:
1. Department of Mathematics Faculty of Sciences Dhar El Mahraz University Sidi Mohamed Ben Abdellah, Atlas Fez, Morocco
Abstract
This manuscript discusses the existence of nontrivial weak solution for the following nonlinear eigenvalue problem driven by the p(?)-biharmonic operator with Rellich-type term {?(|?u|p(x)?2?u) = ?|u|q(x)?2u/?(x)2q(x), for x ? ?, u = ?u = 0, for x ? ??. Considering the case 1 < min x?? p(x) ? max x?? p(x) < min x?? q(x) ? max x?? q(x) < min (N 2, Np(x) N ? 2p(x) ), we extend the corresponding result of the reference [8], for the case 1 < min x?? q(x) ? max x?? q(x) < min x?? p(x) ? max x?? .p(x) < N 2 . The proofs of the main results are based on the mountain pass theorem
Publisher
National Library of Serbia
Reference20 articles.
1. S.N. Antontsev, S.I. Shmarev, A model porous medium equation with variable exponent of nonlinearity: Existence, uniqueness and localization properties of solutions, Nonlinear Anal. Theory Methods Appl. 60 (2005) 515-545.
2. A. Ayoujil, A.R. El Amrouss, On the spectrum of a fourth order elliptic equation with variable exponent, Nonlinear Anal. Theory Methods Appl. 71 (2009) 4916-4926.
3. E. Azroul, M. Bouziani, H. Hjiaj, A. Youssfi, Existence of solutions for some quasilinear ⃗p(x)-elliptic problem with Hardy potential, Mathematica Bohemica. 144 (2019), as doi: 10.21136/MB.2018.0093-17.
4. S. Benbernou, S. Gala, M.A. Ragusa, On the regularity criteria for the 3D magnetohydrodynamic equations via two components in terms of BMO space, Mathematical Methods in the Applied Sciences. 37 (2014) 2320-2325.
5. Y. Chen, S. Levine, M. Rao, Variable exponent linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006) 1383-1406.
Cited by
1 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