Yuxia Guo
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Yuxia Guo has a total of 24 co-authors. Here are the top co-authors by number of shared publications:
- Shusen Yan
The University of New England
5 shared publications Bo Li
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China
4 shared publications- Zhongwei Tang
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing, China
4 shared publications - Jiaquan Liu
Peking University
3 shared publications - Shuangjie Peng
School of Mathematics and Statistics, Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
3 shared publications - Angela Pistoia
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Roma, Italy
1 shared publication
Latest Publications
- Open Access
- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 18 (5) , 2693-2715
Concentration of ground state solutions for quasilinear Schrödinger systems with critical exponents
This paper is concerned with the critical quasilinear Schrödinger systems in \begin{document}$ {\Bbb R}^N: $\end{document}$ \left\{\begin{array}{ll}-\Delta w+(\lambda a(x)+1)w-(\Delta|w|^2)w = \frac{p}{p+q}|w|^{p-2}w|z|^q+\frac{\alpha}{\alpha+\beta}|w|^{\alpha-2}w|z|^\beta\\\ -\Delta z+(\lambda b(x)+1)z-(\Delta|z|^2)z = \frac{q}{p+q}|w|^p|z|^{q-2}z+\frac{\beta}{\alpha+\beta}|w|^\alpha|z|^{\beta-2}z, \ \end{array}\right. $where \begin{document}$ \lambda>0 $\end{document} is a parameter, \begin{document}$ p>2, q>2, \alpha>2, \beta>2, $\end{document} \begin{document}$ 2\cdot(2^*-1) < p+q<2\cdot2^* $\end{document} and \begin{document}$ \alpha+ \beta = 2\cdot2^*. $\end{document} By using variational method, we prove the existence of positive ground state solutions which localize near the set \begin{document}$ \Omega = int \left\{a^{-1}(0)\right\}\cap int \left\{b^{-1}(0)\right\} $\end{document} for \begin{document}$ \lambda $\end{document} large enough.- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 18 (5) , 2693-2715
Open AccessConcentration of ground state solutions for quasilinear Schrödinger systems with critical exponents
This paper is concerned with the critical quasilinear Schrödinger systems in \begin{document}$ {\Bbb R}^N: $\end{document}$ \left\{\begin{array}{ll}-\Delta w+(\lambda a(x)+1)w-(\Delta|w|^2)w = \frac{p}{p+q}|w|^{p-2}w|z|^q+\frac{\alpha}{\alpha+\beta}|w|^{\alpha-2}w|z|^\beta\\\ -\Delta z+(\lambda b(x)+1)z-(\Delta|z|^2)z = \frac{q}{p+q}|w|^p|z|^{q-2}z+\frac{\beta}{\alpha+\beta}|w|^\alpha|z|^{\beta-2}z, \ \end{array}\right. $where \begin{document}$ \lambda>0 $\end{document} is a parameter, \begin{document}$ p>2, q>2, \alpha>2, \beta>2, $\end{document} \begin{document}$ 2\cdot(2^*-1) < p+q<2\cdot2^* $\end{document} and \begin{document}$ \alpha+ \beta = 2\cdot2^*. $\end{document} By using variational method, we prove the existence of positive ground state solutions which localize near the set \begin{document}$ \Omega = int \left\{a^{-1}(0)\right\}\cap int \left\{b^{-1}(0)\right\} $\end{document} for \begin{document}$ \lambda $\end{document} large enough. - 26 November 2018
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 58 (1) , 2
Multiple solutions for critical quasilinear elliptic equations
- 26 November 2018
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 58 (1) , 2
Multiple solutions for critical quasilinear elliptic equations
- 1 October 2018
- Published by Elsevier in Nonlinear Analysis: Real World Applications
- Vol. 43, 378-406
Infinitely many solutions for quasilinear systems with critical exponent
- 1 October 2018
- Published by Elsevier in Nonlinear Analysis: Real World Applications
- Vol. 43, 378-406
Infinitely many solutions for quasilinear systems with critical exponent
- 29 June 2018
- Published by Science China Press., Co. Ltd. in SCIENTIA SINICA Mathematica
- Vol. 49 (1) , 21
Solutions of biharmonic equations with steep potential wells
- 29 June 2018
- Published by Science China Press., Co. Ltd. in SCIENTIA SINICA Mathematica
- Vol. 49 (1) , 21
Solutions of biharmonic equations with steep potential wells
- Open Access
Infinitely many non-radial solutions to a critical equation on annulus
In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \begin{equation*} \left\{\begin{array}{rlll} -\Delta u&=|u|^{\frac{4}{N-2}}u, &\hbox{ in }\Omega,\\ u&=0, &\hbox{ on }\partial\Omega. \end{array}\right. \eqno(P) \end{equation*} on the annulus $\Omega:=\{x\in \mathbb{R}^N: a<|x|<b\}$, $N\geq 3.$ In particular, for any integer $k$ large enough, we build a non-radial solution which look like the unique positive solution $u_0$ to $(P)$ crowned by $k$ negative bubbles arranged on a regular polygon with radius $r_0$ such that $r_0^{\frac{N-2}{2}}u_0(r_0)=:\displaystyle\max_{a\leq r\leq b}r^{\frac{N-2}{2}}u_0(r).$Open AccessInfinitely many non-radial solutions to a critical equation on annulus
In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \begin{equation*} \left\{\begin{array}{rlll} -\Delta u&=|u|^{\frac{4}{N-2}}u, &\hbox{ in }\Omega,\\ u&=0, &\hbox{ on }\partial\Omega. \end{array}\right. \eqno(P) \end{equation*} on the annulus $\Omega:=\{x\in \mathbb{R}^N: a<|x|<b\}$, $N\geq 3.$ In particular, for any integer $k$ large enough, we build a non-radial solution which look like the unique positive solution $u_0$ to $(P)$ crowned by $k$ negative bubbles arranged on a regular polygon with radius $r_0$ such that $r_0^{\frac{N-2}{2}}u_0(r_0)=:\displaystyle\max_{a\leq r\leq b}r^{\frac{N-2}{2}}u_0(r).$ - 18 December 2017
- Published by IOP Publishing in Nonlinearity
- Vol. 31 (1) , 314-339
The existence, uniqueness and nonexistence of the ground state to the N-coupled Schrödinger systems in *
Consider the following Schrödinger system: where either Ω = R n ( n = 2 , 3 , 4 ) or Ω ⊂ R 4 is a smooth bounded domain. Note that the cubic nonlinearities and the coupling terms are of critical growth whenever dimension n = 4 . We give a characterization of the least energy solutions when Ω = R n ( n = 2 , 3 ) or Ω is a smooth bounded domain of R 4 , if the coupling matrix B := ( β i j ) is positively or negatively definite with β i j ⩾ 0 , β k k > 0 , ∀ k ; i ≠ j ; and B − 1 = ( β i j ) − 1 = ( a i j ) exists and satisfies ∑ j a i j > 0 for i = 1 , 2 , . . . , N . Furthermore, when Ω = R 4 and λ j = 0 , j = 1 , 2 , . . . , N , we obtain a nonexistence theorem about the least energy solutions provided attraction and repulsion coexist, i.e. some of β i j , i ≠ j are positive but some others are negative.
- 18 December 2017
- Published by IOP Publishing in Nonlinearity
- Vol. 31 (1) , 314-339
The existence, uniqueness and nonexistence of the ground state to the N-coupled Schrödinger systems in *
Consider the following Schrödinger system: where either Ω = R n ( n = 2 , 3 , 4 ) or Ω ⊂ R 4 is a smooth bounded domain. Note that the cubic nonlinearities and the coupling terms are of critical growth whenever dimension n = 4 . We give a characterization of the least energy solutions when Ω = R n ( n = 2 , 3 ) or Ω is a smooth bounded domain of R 4 , if the coupling matrix B := ( β i j ) is positively or negatively definite with β i j ⩾ 0 , β k k > 0 , ∀ k ; i ≠ j ; and B − 1 = ( β i j ) − 1 = ( a i j ) exists and satisfies ∑ j a i j > 0 for i = 1 , 2 , . . . , N . Furthermore, when Ω = R 4 and λ j = 0 , j = 1 , 2 , . . . , N , we obtain a nonexistence theorem about the least energy solutions provided attraction and repulsion coexist, i.e. some of β i j , i ≠ j are positive but some others are negative.
- Open Access
Uniqueness of planar vortex patch in incompressible steady flow
We investigate a steady planar flow of an ideal fluid in a bounded simple connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two methods to deal with the existence of solutions for this problem: the vorticity method and the stream function method. A long standing open problem is whether these two entirely different methods result in the same solution. In this paper, we will give a positive answer to this problem by studying the local uniqueness of the solutions. Another result obtained in this paper is that if the domain is convex, then the vortex patch problem has a unique solution.
Open AccessUniqueness of planar vortex patch in incompressible steady flow
We investigate a steady planar flow of an ideal fluid in a bounded simple connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two methods to deal with the existence of solutions for this problem: the vorticity method and the stream function method. A long standing open problem is whether these two entirely different methods result in the same solution. In this paper, we will give a positive answer to this problem by studying the local uniqueness of the solutions. Another result obtained in this paper is that if the domain is convex, then the vortex patch problem has a unique solution.
- 6 March 2017
- Published by Wiley in Proceedings of the London Mathematical Society
- Vol. 114 (6) , 1005-1043
Local uniqueness and periodicity induced by concentration
- 6 March 2017
- Published by Wiley in Proceedings of the London Mathematical Society
- Vol. 114 (6) , 1005-1043
Local uniqueness and periodicity induced by concentration
- 16 January 2017
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 147 (2) , 371-396
Infinitely many non-radial solutions for the polyharmonic Hénon equation with a critical exponent
We study the following polyharmonic Hénon equation: where (m)* = 2N/(N – 2m) is the critical exponent, B1(0) is the unit ball in ℝN, N ⩾ 2m + 2 and K(|y|) is a bounded function. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.
- 16 January 2017
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 147 (2) , 371-396
Infinitely many non-radial solutions for the polyharmonic Hénon equation with a critical exponent
We study the following polyharmonic Hénon equation: where (m)* = 2N/(N – 2m) is the critical exponent, B1(0) is the unit ball in ℝN, N ⩾ 2m + 2 and K(|y|) is a bounded function. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.
- Open Access
- 1 January 2016
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 36 (12) , 6873-6898
Infinitely many non-radial solutions for the prescribed curvature problem of fractional operator
We consider the following problem: \begin{equation*} \left\{\begin{array}{ll} (-\Delta)^s u=K(y)u^{p-1} \hbox { in } \ \mathbb{R}^N, \\ u>0, \ y \in \mathbb{R}^N, \end{array}\right. (P) \end{equation*} where $s\in(0,\frac{1}{2})$ for $N=3$, $s\in(0,1)$ for $N\geq4$ and $p=\frac{2N}{N-2s}$ is the fractional critical Sobolev exponent. Under the condition that the function $K(y)$ has a local maximum point, we prove the existence of infinitely many non-radial solutions for the problem $(P)$.- 1 January 2016
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 36 (12) , 6873-6898
Open AccessInfinitely many non-radial solutions for the prescribed curvature problem of fractional operator
We consider the following problem: \begin{equation*} \left\{\begin{array}{ll} (-\Delta)^s u=K(y)u^{p-1} \hbox { in } \ \mathbb{R}^N, \\ u>0, \ y \in \mathbb{R}^N, \end{array}\right. (P) \end{equation*} where $s\in(0,\frac{1}{2})$ for $N=3$, $s\in(0,1)$ for $N\geq4$ and $p=\frac{2N}{N-2s}$ is the fractional critical Sobolev exponent. Under the condition that the function $K(y)$ has a local maximum point, we prove the existence of infinitely many non-radial solutions for the problem $(P)$.