Detail publikace

Planar Schrodinger equations with critical exponential growth

CHEN, S. RADULESCU, V. TANG, X. WEN, L.

Originální název

Planar Schrodinger equations with critical exponential growth

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

In this paper, we study the following quasilinear Schrodinger equation: -epsilon(2)Delta u + V(x)u - epsilon(2)Delta(u(2))u = g(u), x is an element of R-2, where epsilon > 0 is a small parameter, V is an element of C(R-2, R) is uniformly positive and allowed to be unbounded from above, and g is an element of C(R, R) has a critical exponential growth at infinity. In the autonomous case, when epsilon > 0 is fixed and V(x) equivalent to V-0 is an element of R+, we first present a remarkable relationship between the existence of least energy solutions and the range of V-0 without any monotonicity conditions on g. Based on some new strategies, we establish the existence and concentration of positive solutions for the above singularly perturbed problem. In particular, our approach not only permits to extend the previous results to a wider class of potentials V and source terms g, but also allows a uniform treatment of two kinds of representative nonlinearities that g has extra restrictions at infinity or near the origin, namely lim inf(|t|->+infinity)tg(t)/e(0)(alpha)t4 or g(u) >= C-q,C-V u(q-1) with q > 4 and C-q,C- V > 0 is an implicit value depending on q, V and the best constant of the embedding H-1(R-2) subset of L-q(R-2), considered in the existing literature. To the best of our knowledge, there have not been established any similar results, even for simpler semilinear Schrodinger equations. We believe that our approach could be adopted and modified to treat more general elliptic partial differential equations involving critical exponential growth.

Klíčová slova

LINEAR ELLIPTIC-EQUATIONS;GROUND-STATE SOLUTION;SOLITON-SOLUTIONS;NONTRIVIAL SOLUTION;POSITIVE SOLUTIONS;EXISTENCE;INEQUALITIES;R-2

Autoři

CHEN, S.; RADULESCU, V.; TANG, X.; WEN, L.

Vydáno

11. 12. 2024

ISSN

0944-2669

Periodikum

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Ročník

63

Číslo

9

Stát

Spojené státy americké

Strany počet

46

URL

https://doi.org/10.1007/s00526-024-02852-z

BibTex

@article{BUT191299,
  author="Sitong {Chen} and Vicentiu {Radulescu} and Xianhua {Tang} and Lixi {Wen}",
  title="Planar Schrodinger equations with critical exponential growth
",
  journal="CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS",
  year="2024",
  volume="63",
  number="9",
  pages="46",
  doi="10.1007/s00526-024-02852-z",
  issn="0944-2669",
  url="https://doi.org/10.1007/s00526-024-02852-z"
}