Multiple solutions to logarithmic Schrödinger equations with periodic potential

By Marco Squassina, A. Szulkin. 2014

166 citations recorded by the source corpus.

We study a class of logarithmic Schrödinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/499ce423e43242e0eb74251b5c41552f75ad5627

How researchers see this paper

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In Applied Mathematics

1. Chao Ji
2. A. Szulkin
3. Xianhua Tang
4. X. Tang
5. Yanheng Ding
6. Louis Jeanjean

In Computational Theory and Mathematics

1. Chao Ji
2. A. Szulkin
3. X. Tang
4. Xianhua Tang
5. Yanheng Ding

In Mathematical Physics

1. Chao Ji
2. A. Szulkin
3. Xianhua Tang
4. X. Tang
5. Yanheng Ding
6. Louis Jeanjean

Citations in the corpus

• A logarithmic Schrödinger equation with asymptotic conditions on the potential (2015, background): “u2 ∈ L1(RN) (i.e., J(u) < ∞) and Z R N (∇u ·∇v +V (x)uv)dx = Z R uvlogu2 dx for all v ∈ C∞ 0 (R N). Local estimates and standard bootstrap arguments show that such u is a classical solution. As in [16], we set F1(s) := ˆ −1 2s 2 logs2, |s| < δ, −1 2s 2(logδ2 +3) +2δ|s| − 1 2δ 2, |s| > δ, an”