In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on R<sup>N</sup> × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a sm...In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on R<sup>N</sup> × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, I<sub>α</sub> is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique. .展开更多
In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger...In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.展开更多
This paper is considered the existence of positive solutions for a class of generalized quasilinear Schrödinger equations with nonlocal term in R<sup>N</sup> which have appeared from plasma physic...This paper is considered the existence of positive solutions for a class of generalized quasilinear Schrödinger equations with nonlocal term in R<sup>N</sup> which have appeared from plasma physics, as well as high-power ultrashort laser in matter. We use a charge of variables and obtain the existence of solutions via minimization argument.展开更多
The original online version of this article (Liao, P., Ping, R. and Chen, S. (2022) Positive Solutions for a Class of Quasilinear Schrödinger Equations with Nonlocal Term. Journal of Applied Mathematics and P...The original online version of this article (Liao, P., Ping, R. and Chen, S. (2022) Positive Solutions for a Class of Quasilinear Schrödinger Equations with Nonlocal Term. Journal of Applied Mathematics and Physics, 10, 347-359. https://doi.org/10.4236/jamp.2022.102027) needs some further amendments and clarification.展开更多
文摘In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on R<sup>N</sup> × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, I<sub>α</sub> is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique. .
文摘In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.
文摘This paper is considered the existence of positive solutions for a class of generalized quasilinear Schrödinger equations with nonlocal term in R<sup>N</sup> which have appeared from plasma physics, as well as high-power ultrashort laser in matter. We use a charge of variables and obtain the existence of solutions via minimization argument.
文摘The original online version of this article (Liao, P., Ping, R. and Chen, S. (2022) Positive Solutions for a Class of Quasilinear Schrödinger Equations with Nonlocal Term. Journal of Applied Mathematics and Physics, 10, 347-359. https://doi.org/10.4236/jamp.2022.102027) needs some further amendments and clarification.
