On the least energy solutions of nonlinear Schrödinger equations with electromagnetic fields

✍ Scribed by Zhongwei Tang

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 257 KB
• Volume: 54
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2006.12.031

✦ Synopsis

In this paper, we are concerned with the existence of least energy solutions of nonlinear Schrödinger equations with electromagnetic fields

for sufficiently large λ, where i is the imaginary unit, 2 < p < 2N N -2 for N ≥ 3 and 2 < p < +∞ for N = 1, 2. a(x) is a real continuous function on R N , and A(x) = (A 1 (x), A 2 (x), . . . , A N (x)) is such that A j (x) is a real local Hölder continuous function on R N for j = 1, 2, . . . , N . Using variational methods we prove the existence of least energy solution u(x) which localizes near the potential well int(a -1 (0)) for λ large.