We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional...We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional potential Calogero-Bogoyavlenskii- Schiff （CBS） equation and Konopelchenko-Dubrovsky （KD） equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, re-spectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables.展开更多
In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the...In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the Painlev^-Kuratowski Convergence of the weak efficient solution sets and efficient solution sets for the perturbed vector equilibrium problems with a sequence of mappings converging in real linear metric spaces. These results extend and improve some known results in the literature.展开更多
In this paper, the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w（x） = /x/2αe-（x4＋tx2）, x ∈R, where α is a constant larger than - 1/2 and t...In this paper, the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w（x） = /x/2αe-（x4＋tx2）, x ∈R, where α is a constant larger than - 1/2 and t is any real number. They consider this problem in three separate cases： （i） c 〉 -2, （ii） c = -2, and （iii） c 〈 -2, where c ：= tN-1/2 is a constant, N = n ＋ a and n is the degree of the polynomial. In the first two cases, the support of the associated equilibrium measure μ is a single interval, whereas in the third case the support of μt consists of two intervals. In each case, globally uniform asymptotic expansions are obtained in several regions. These regions together cover the whole complex plane. The approach is based on a modified version of the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou （1993）.展开更多
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2011AQ017 and ZR2010AM028)the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No.13CX02010A)
文摘We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional potential Calogero-Bogoyavlenskii- Schiff （CBS） equation and Konopelchenko-Dubrovsky （KD） equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, re-spectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables.
基金Supported by the National Natural Science Foundation of China(No.11301571.11271389.11271391)the Natural Science Foundation Project of ChongQing(No.CSTC,2012jjA00016.2011BA0030)the Education Committee Research Foundation of ChongQing(KJ130428)
文摘In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the Painlev^-Kuratowski Convergence of the weak efficient solution sets and efficient solution sets for the perturbed vector equilibrium problems with a sequence of mappings converging in real linear metric spaces. These results extend and improve some known results in the literature.
基金supported by the National Natural Science Foundation of China(Nos.11771090,11571376)
文摘In this paper, the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w（x） = /x/2αe-（x4＋tx2）, x ∈R, where α is a constant larger than - 1/2 and t is any real number. They consider this problem in three separate cases： （i） c 〉 -2, （ii） c = -2, and （iii） c 〈 -2, where c ：= tN-1/2 is a constant, N = n ＋ a and n is the degree of the polynomial. In the first two cases, the support of the associated equilibrium measure μ is a single interval, whereas in the third case the support of μt consists of two intervals. In each case, globally uniform asymptotic expansions are obtained in several regions. These regions together cover the whole complex plane. The approach is based on a modified version of the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou （1993）.
