Multibump solutions for quasilinear elliptic equations with critical growth

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4830027· OSTI ID:22251783

Liu, Jiaquan ^[1]; Wang, Zhi-Qiang ^[2]; Wu, Xian ^[3]

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1. LMAM, School of Mathematical Science, Peking University, Beijing 100871 (China)
2. Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China and Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322 (United States)
3. Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092 (China)

The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrödinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217–1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040–4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions.

• OSTI ID: 22251783
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
EQUATIONS
GROUND STATES
MATHEMATICAL SOLUTIONS
PERIODICITY
POTENTIALS
QUASILINEAR PROBLEMS