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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]

In this paper we consider the fourth-order problem{Δ2u=µ|u|s-1u+|u|2\*-2uinΩ,u,-Δu>0in Ω,u,Δu=0on ∂Ω, where Ω is a smooth bounded domain in RN, N≥5 and 2\*=2N/(N-4). We assume 2≤s+1<2\* in case N≥8 and 2\*-20 is sufficiently small. [ABSTRACT FROM AUTHOR]

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

Abstract: In this paper, existence results of positive solutions to a Neumann problem involving the p-Laplacian are established. Multiplicity results are also pointed out. The approach is based on variational methods. [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: In this paper, the authors prove some inequalities for the generalized elliptic integrals with respect to Hölder means. [Copyright &y& Elsevier]

Abstract: For fixed u and v such that , the monotonicity of the quotients of Jacobi theta functions, namely, , , on has been established in the previous works of A.Yu. Solynin, K. Schiefermayr, and Solynin and the first author. In the present paper, we show that the quotients and are convex on . [Copyright &y& Elsevier]

Abstract: In this paper we are concerned with the number of nonnegative solutions of the elliptic system where is a bounded smooth domain, , and , and , are the partial derivatives of the homogeneous functions , where . In the proofs we apply variational methods and Ljusternik–Schnirelmann theory. [Copyright &y& Elsevier]

Abstract: This paper deals with some fourth-order elliptic equations with Navier boundary condition. By using the variational method, some existence and multiplicity results are established. [Copyright &y& Elsevier]

Abstract: In this paper, we study the relationship between the generalized Hersch–Pfluger distortion function and complete elliptic integrals of the second kind , and establish several inequalities for and . [Copyright &y& Elsevier]

Abstract: In this paper, we show that semilinear elliptic systems of the form possess at least one nontrivial solution pair , where λ and μ are positive numbers, and are continuous functions on and asymptotically linear as . [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to prove the existence of a unique classical solution to the quasilinear elliptic equation , where at and where on the boundary ∂Ω. We prove that if the functions a, f, v, g satisfy certain conditions, then a unique classical solution exists. Applications include stationary heat/diffusion problems with convection and with a source/sink, where the value of the solution is known at a spatial location , and where is known on the boundary. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence of positive solutions to the class of elliptic problems with critical growth type where λ is a positive parameter, is a function of class and are continuous functions. [Copyright &y& Elsevier]

Abstract: This paper does for combinations of theta functions most of what Carlson (2004) did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters c, d, n for the Jacobian case but now in the subscripts 2, 3, 4 for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas. [Copyright &y& Elsevier]

Abstract: In this paper we determine the exact asymptotic behavior of the principal eigenvalue of a mixed elliptic eigenvalue problem which depends on a positive parameter λ when . We analyze the case in which the problem is considered in a smooth bounded domain Ω of , and also the case of planar domains which are smooth except for a finite number of corner points. [ABSTRACT FROM AUTHOR]

Abstract: This research is a continuation of a recent paper due to the first four authors. Shared value problems related to a meromorphic function and its shift , where , are studied. It is shown, for instance, that if is of finite order and shares two values CM and one value IM with its shift , then f is a periodic function with period c. The assumption on the order of f can be dropped if f shares two shifts in different directions, leading to a new way of characterizing elliptic functions. The research findings also include an analogue for shifts of a well-known conjecture by Brück concerning the value sharing of an entire function f with its derivative . [Copyright &y& Elsevier]

Abstract: In this paper, we study the following problem where is either asymptotically linear or superlinear with respect to t at infinity. The Ambrosetti–Rabinowitz type condition, that is so-called (AR) condition: as well as the monotonicity of are not assumed. Under appropriate assumptions on and f, we prove that problem (0.1) has at least two positive solutions. [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 consider the existence of positive, negative and sign-changing solutions for some fourth order semilinear elliptic boundary value problems. We present new results on invariant sets of the gradient flows of the corresponding variational functionals. The structure of the invariant sets will be built into minimax procedures to construct the sign-changing solutions. [Copyright &y& Elsevier]

Abstract: Let E be a subset of . We say that is an E-Pólya frequency function if the kernel is totally positive on and f is integrable on . In this paper, we show that under some conditions on E, an E-Pólya frequency function is a Pólya frequency function. This strengthens Schoenberg''s result on Pólya frequency functions. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence of infinitely many solutions of noncooperative elliptic systems perturbed from odd cases. [Copyright &y& Elsevier]