Existence of solutions for a quasilinear elliptic system with local nonlinearity on ℝN. (30th June 2021)

• Record Type: Journal Article
• Authors: Zhang, Xingyong; Liu, Cuiling
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 17(2021)
• Page Start: 13186
• Page End: 13212
• Publication Date: 2021-06-30
• Subjects: cutoff technique -- local nonlinearity near origin -- Moser iteration technique -- mountain pass theorem -- quasilinear elliptic system; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7617
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we investigate the existence of solutions for a class of quasilinear elliptic system. By developing the Moser iteration technique, we obtain that system has a nontrivial solution ( u λ, v λ ) with ‖( u λ, v λ )‖ ∞ ≤ 2 for every λ large enough when the nonlinear term F satisfies some growth conditions only in a circle with center 0 and radius 4, and the families of solutions {( u λ, v λ )} satisfy that ‖( u λ, v λ ) ‖ → 0 as λ → ∞ . Moreover, because the interaction of u and v in elliptic system causes that the estimate of ‖ u ‖ ∞ cannot vary with ‖ u ‖, the conclusion for the elliptic system is weaker than the corresponding result for the quasilinear elliptic equation, which is given in the end as a comparison.