Search

Abstract: In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321–339] via gradient estimate and discuss an application to the Lamé system. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a necessary and sufficient condition for the convexity of the complete elliptic integrals of the first kind with respect to Hölder means. [Copyright &y& Elsevier]

Abstract: Let be a fixed number. A function is said to be a-shift-generating (a-SG) if for every , is a totally positive sequence and it does not coincide with a sequence of the form , where and . In this paper, we describe all a-SG functions and obtain a new characterization of totally positive functions in the terms of a-SG functions. In addition, using characteristic properties of a-SG functions, we generalize the famous Jacobian identity in theory of elliptic functions. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations , , . We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy . The asymptotic behavior of solutions is also described. [Copyright &y& Elsevier]

Abstract: In this paper, we study the uniqueness problems on entire functions sharing one value with the same multiplicities. We generalize and unify some previous results of Fang and Hua [M.L. Fang, X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly 13 (1) (1996) 44–48], Yang and Hua [C.C. Yang, X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (2) (1997) 395–406] and Fang [M.L. Fang, Uniqueness and value-sharing of entire functions, Comput. Math. Appl. 44 (2002) 828–831]. [Copyright &y& Elsevier]

Abstract: In this paper, assume that h is nonnegative and , we prove that if is sufficiently small, then there are at least three positive solutions of Eq. (1) in an exterior cylinder domain. [Copyright &y& Elsevier]