Yuhua Sun

Analysis on Manifolds and PDEs

Partial Differential Equation, Calculus, Linear Algebra, Ordinary Differential Equation

1.Sharp criteria for nonlocal elliptic inequalities on manifolds, submitted.(with Q. Gu, X. Huang)

2.On positive solutions of biharmonic elliptic inequalities on Riemannian manifolds, submitted.(with Y. Zheng)

3.A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms, submitted, arXiv:2205.07484. (with R. Filippucci, Y. Zheng)

4.Sharp Liouville type results for semilinear elliptic inequalities involving gradient terms on weighted graphs, submitted, arXiv: 2205.06047. (with L. Hao)

5.Nonexistence for parabolic differential inequalities with convection terms in exterior domains, submitted. (with M. Jleli, B. Samet)

6.On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds, to appear in Geometric Potential Analysis - AAG 6, De Gruyter. (with F. Xu)

7.Seminlinear differential inequalities on weighted graph, submitted, arXiv:2201.06397. (with Q. Gu, X. Huang)

8.Fractional $(p,\opm)$-Laplace's Equations and Inequalities, submitted.(with L. Liu, J. Xiao)

9.A sharp Liouville principle for $\Delta_mu+u^p|\nabla u|^q\le 0$ on geodesically complete noncompact Riemannian manifolds, accepted by Mathematische Annalen, Doi: 10.1007/s00208-021-02311-6. (with J. Xiao, F. Xu)

10.ed. A. Grigor'yan, Y. Sun, Analysis and partial differential equations on manifolds, fractals and graphs, de Gruyter series Advances in Analysis and Geometry 3, 2021. https://www.degruyter.com/view/title/578846?language=en

11.On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds, Advances in Analysis and Geometry 3, de Gruyter.(with F. Xu)

12.Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold, to appear in Calc. Var. PDEs 59,Article number:170(2020). (with Q. Gu, J. Xiao, F. Xu)

13.Superlinear elliptic inequalities on manifolds, J. Func. Anal. 278(2020), no. 9, 108444.(with A. Grigor’yan, I. Verbitsky)

14.On positive solutions of semilinear elliptic inequalities on Riemannian manifolds, Calc. Var. PDEs. 58(2019),no. 6, Art.207, 30pp.(with A. Grigor’yan)

15.Liouville type theorems forsystems of elliptic differential inequalities on Riemannian manifolds, J. Math. Anal. Appl. Vol. 466(2018), No.1, 426-446.(with F. Xu, L. Wang)

16.Absence of positive solutions to the system of differential inequalities on manifolds, J. Math. Phys. 59(2018), 011510.

17.Nonexistence results for systems of elliptic and parabolic differential inequalities in exterior domains of R^n, Pacific J. Math, Vol. 293 (2018), No. 1, 245–256.

18.Absence of nonnegative solutions to the system of differential inequalities on manifolds, J. Math. Anal. Appl.,450(2017), no. 2, 901–914.

19.The absence of global positive solutions to semilinear parabolic differential inequalities in exterior domain, Proc. Amer. Math. Soc. 145 (2017), no. 8, 3455–3464.

20.Uniqueness result on nonnegative solutions of a large class of differential inequalities on Riemannian manifolds. Pacific J. Math. 280 (2016), no. 1, 241–254.

21.On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds. Comm. Pure Appl. Anal. 14 (2015), no. 5, 1743–1757.

22.On nonexistence of positive solutions of quasi-linear inequality on Riemannian manifolds. Proc. Amer. Math. Soc. 143 (2015), no. 7, 2969–2984.

23.Uniqueness result for non-negative solutions of semi-linear inequalities on Riemannian manifolds. J. Math. Anal. Appl. 419 (2014), no. 1, 643–661.

24.On non-negative solutions of the inequality ∆u+u^σ≤0 on Riemannian manifolds, Comm. Pure Appl. Math., Vol.67(2014), Issue. 8, 1336-1352.(with A.Grigor'yan)

25.Inhomogeneous parabolic equations on unbounded metric measure spaces, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 5, 1003–1025.(with K.J.Falconer, J. Hu)

26.Heat flow method for Lichnerowicz type equations on closed manifolds, Z. Angew. Math. Phys. 63 (2012), no. 2, 261–270.(with L. Ma, X. Tang)

1.Sharp criteria for nonlocal elliptic inequalities on manifolds, submitted.(with Q. Gu, X. Huang)

2.On positive solutions of biharmonic elliptic inequalities on Riemannian manifolds, submitted.(with Y. Zheng)

3.A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms, submitted, arXiv: 2205.07484. (with R. Filippucci, Y. Zheng)

4.Sharp Liouville type results for semilinear elliptic inequalities involving gradient terms on weighted graphs,  to appear in DCDS-S. (with L. Hao)

5.Higher order evolution inequalities with convection terms in an exterior domain of R^N, J. Math. Anal. Appl. Volume 519, Issue 1, 1 March 2023, 126738. (with M. Jleli, B. Samet)

6.On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds, to appear in Geometric Potential Analysis - AAG 6, De Gruyter. (with F. Xu)

7.Seminlinear differential inequalities on weighted graph, submitted, to appear in CVPDE, Doi:10.1007/s00526-022-02384-4. (with Q. Gu, X. Huang)

8.Quasilinear Laplace Equations and Inequalities with Fractional Orders, to appear in Mathematische Annalen, https://doi.org/10.1007/s00208-022-02510-9.(with L. Liu, J. Xiao)

9.A sharp Liouville principle for $\Delta_mu+u^p|\nabla u|^q\le 0$ on geodesically complete noncompact Riemannian manifolds, Math. Ann. 384 (2022), no. 3-4, 1309–1341. (with J. Xiao, F. Xu)

10.ed. A. Grigor'yan, Y. Sun, Analysis and partial differential equations on manifolds, fractals and graphs, de Gruyter series Advances in Analysis and Geometry 3, 2021. https://www.degruyter.com/view/title/578846?language=en

11.On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds, Advances in Analysis and Geometry 3, de Gruyter.(with F. Xu)

12.Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold,  Calc. Var. PDEs 59,Article number:170(2020). (with Q. Gu, J. Xiao, F. Xu)

13.Superlinear elliptic inequalities on manifolds, J. Func. Anal. 278(2020), no. 9, 108444.(with A. Grigor’yan, I. Verbitsky)

14.On positive solutions of semilinear elliptic inequalities on Riemannian manifolds, Calc. Var. PDEs. 58(2019),no. 6, Art.207, 30pp.(with A. Grigor’yan)

15.Liouville type theorems forsystems of elliptic differential inequalities on Riemannian manifolds, J. Math. Anal. Appl. Vol. 466(2018), No.1, 426-446.(with F. Xu, L. Wang)

16.Absence of positive solutions to the system of differential inequalities on manifolds, J. Math. Phys. 59(2018), 011510.

17.Nonexistence results for systems of elliptic and parabolic differential inequalities in exterior domains of R^n, Pacific J. Math, Vol. 293 (2018), No. 1, 245–256.

18.Absence of nonnegative solutions to the system of differential inequalities on manifolds, J. Math. Anal. Appl.,450(2017), no. 2, 901–914.

19.The absence of global positive solutions to semilinear parabolic differential inequalities in exterior domain, Proc. Amer. Math. Soc. 145 (2017), no. 8, 3455–3464.

20.Uniqueness result on nonnegative solutions of a large class of differential inequalities on Riemannian manifolds. Pacific J. Math. 280 (2016), no. 1, 241–254.

21.On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds. Comm. Pure Appl. Anal. 14 (2015), no. 5, 1743–1757.

22.On nonexistence of positive solutions of quasi-linear inequality on Riemannian manifolds. Proc. Amer. Math. Soc. 143 (2015), no. 7, 2969–2984.

23.Uniqueness result for non-negative solutions of semi-linear inequalities on Riemannian manifolds. J. Math. Anal. Appl. 419 (2014), no. 1, 643–661.

24.On non-negative solutions of the inequality ∆u+u^σ≤0 on Riemannian manifolds, Comm. Pure Appl. Math., Vol.67(2014), Issue. 8, 1336-1352.(with A.Grigor'yan)

25.Inhomogeneous parabolic equations on unbounded metric measure spaces, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 5, 1003–1025.(with K.J.Falconer, J. Hu)