Prof. Yongxiang Li

Department of Mathematics, Northwest Normal University, China.

Prof. Yongxiang Li

Department of Mathematics, Northwest Normal University, China.

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Academic Career Length

24Years (2003-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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25 February 2020 in Fractional Calculus and Applied Analysis

Journal Article

Existence and Approximate Controllability of Fractional Evolution Equations with Nonlocal Conditions Via Resolvent Operators

XZ

1 January 2018 in Communications on Pure and Applied Analysis

Journal Article

A blowup alternative result for fractional nonautonomous evolution equation of Volterra type

XZ

In this article, we consider a class of fractional non-autonomous integro-differential evolution equation of Volterra type in a Banach space $E$, where the operators in linear part (possibly unbounded) depend on time $t$. Combining the theory of fractional calculus, operator semigroups and measure of noncompactness with Sadovskii's fixed point theorem, we firstly proved the local existence of mild solutions for corresponding fractional non-autonomous integro-differential evolution equation. Based on the local existence result and a piecewise extended method, we obtained a blowup alternative result for fractional non-autonomous integro-differential evolution equation of Volterra type. Finally, as a sample of application, these results are applied to a time fractional non-autonomous partial integro-differential equation of Volterra type with homogeneous Dirichlet boundary condition. This paper is a continuation of Heard and Rakin [13, J. Differential Equations, 1988] and the results obtained essentially improve and extend some related conclusions in this area.

10 August 2013 in Zeitschrift für angewandte Mathematik und Physik

Journal Article

Existence of mild solutions for fractional evolution equations with mixed monotone nonlocal conditions

30 September 2003 in Nonlinear Analysis

Journal Article

Positive solutions of fourth-order periodic boundary value problems

18 August 2018 in Journal of Pseudo-Differential Operators and Applications

Journal Article

Fractional non-autonomous evolution equation with nonlocal conditions

XZ

1 January 2021 in Discrete and Continuous Dynamical Systems-Series B

Journal Article

Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families

XZ

This paper investigates the Cauchy problem to a class of stochastic non-autonomous evolution equations of parabolic type governed by noncompact evolution families in Hilbert spaces. Combining the theory of evolution families, the fixed point theorem with respect to convex-power condensing operator and a new estimation technique of the measure of noncompactness, we established some new existence results of mild solutions under the situation that the nonlinear function satisfy some appropriate local growth condition and a noncompactness measure condition. Our results generalize and improve some previous results on this topic, since the strong restriction on the constants in the condition of noncompactness measure is completely deleted, and also the condition of uniformly continuity of the nonlinearity is not required. At last, as samples of applications, we consider the Cauchy problem to a class of stochastic non-autonomous partial differential equation of parabolic type.

About Me

[1] Yongxiang Li, Positive radial solutions for elliptic equations with nonlinear gradient terms on the unit ball, Mediterranean Journal of Mathematics, 2020, 17(6): No. 176. [2] Yongxiang Li, Yabing Gao. Existence and uniqueness results for the bending elastic beam equations, Applied Mathematics Letters, 2019, 95: 72-77. [3] Yongxiang Li. Positive radial solutions for elliptic equations with nonlinear gradient terms in an annulus, Complex Variables and Elliptic Equations, 2018, 63(2): 171-187. [4] Yongxiang Li. Existence of positive solutions for the cantilever beam equations with fully nonlinear terms, Nonlinear Analysis: Real World Applications, 2016, 27: 221-237. [5] Yongxiang Li, Positive solutions for second order boundary value problems with derivative terms, Mathematische Nachrichten, 2016, 289(16): 2058–2068. [6] Yongxiang Li. Existence and asymptotic stability of periodic solution for evolution equations with delays. J. Functional Analysis, 2011, 261(5): 1309-1324. [7] Yongxiang Li, Hongxia Fan. Existence of positive periodic solutions for higher order ordinary differential equations. Comput. Math. Appl. 2011, 62(4): 1715-1722. [9] Yongxiang Li. Positive periodic solutions for fully third-order ordinary differential equations. Comput. Math. Appl. 2010, 59(11): 3464-3471. [10] Yongxiang Li. Existence and uniqueness of periodic solution for a class of semilinear evolution equations. J. Math. Anal. Appl. 2009, 349(1): 226-234.

[1] Yongxiang Li, Positive radial solutions for elliptic equations with nonlinear gradient terms on the unit ball, Mediterranean Journal of Mathematics, 2020, 17(6): No. 176. [2] Yongxiang Li, Yabing Gao. Existence and uniqueness results for the bending elastic beam equations, Applied Mathematics Letters, 2019, 95: 72-77. [3] Yongxiang Li. Positive radial solutions for elliptic equations with nonlinear gradient terms in an annulus, Complex Variables and Elliptic Equations, 2018, 63(2): 171-187. [4] Yongxiang Li. Existence of positive solutions for the cantilever beam equations with fully nonlinear terms, Nonlinear Analysis: Real World Applications, 2016, 27: 221-237. [5] Yongxiang Li, Positive solutions for second order boundary value problems with derivative terms, Mathematische Nachrichten, 2016, 289(16): 2058–2068. [6] Yongxiang Li. Existence and asymptotic stability of periodic solution for evolution equations with delays. J. Functional Analysis, 2011, 261(5): 1309-1324. [7] Yongxiang Li, Hongxia Fan. Existence of positive periodic solutions for higher order ordinary differential equations. Comput. Math. Appl. 2011, 62(4): 1715-1722. [9] Yongxiang Li. Positive periodic solutions for fully third-order ordinary differential equations. Comput. Math. Appl. 2010, 59(11): 3464-3471. [10] Yongxiang Li. Existence and uniqueness of periodic solution for a class of semilinear evolution equations. J. Math. Anal. Appl. 2009, 349(1): 226-234.