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Classification of Positive Solitary Solutions of the Nonlinear Choquard Equation
AbstractIn this paper, we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary Choquard equation $$\Delta
Convergence for a Liouville equation
Abstract. In this paper, we study the asymptotic behavior of solutions of the Dirichlet problem for the Liouville equation ¶¶ $ -\Delta u= \lambda {{K(x)e^u} \over {\int_{\Omega}K(x)e^u}} $¶¶on a
A Liouville type Theorem for an integral system
In this paper, we study a conjecture of J.Serrin and give a partial generalized result of the work of de Figueiredo and Felmer about Liouville type Theorem for non-negative solutions for an
On a length preserving curve flow
In this paper, we consider a new length preserving curve flow for closed convex curves in the plane. We show that the flow exists globally, the area of the region bounded by the evolving curve is
Logistic Type Equations on RN by a Squeezing Method Involving Boundary Blow‐Up Solutions
We study, on the entire space RN(N ⩾ 1), the diffusive logistic equation
Mass Under the Ricci Flow
In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is
Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds ✩
In this paper, we study the local gradient estimate for the positive solution to the following equation: u + au logu + bu = 0 in M, where a < 0, b are real constants, M is a complete non-compact