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Minimizers of Caffarelli–Kohn–Nirenberg Inequalities with the Singularity on the Boundary
No full textUniqueness of topological solutions and the structure of solutions for the Chern-Simons system with two Higgs particles
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On the Semilinear Elliptic Equations Δu+β(1+|x|)μup−γ(1+|x|)νuq=0 ((1.1)) in Rn
No full textAbstractIn this paper, we consider the semilinear elliptic equationΔu+β1+|x|μup−γ1+|x|νuqinRn,where n≥3, Δ=∑ni=1(∂2/∂x2i), β and γ are two positive constants, and p,q,μ,ν are constants with q>p>1 and μ≥ν>2. We note that if β=0, γ>0, and ν>2, then the complete classification of all possible positive solutions was conducted by Cheng and Ni [Indiana Univ. Math. J.41 (1992), 261–278]. If γ=0 and β>0, then (1.1) is the so-called Matukuma-type equation, and the solution structures were classified by Li and Ni [Duke Math. J.53 (1985), 895–924] and Ni and Yotsutani [Japan J. Appl. Math.5 (1988), 1–32]. If β>0 and γ>0, then some results about the structure of positive solutions of (1.1) were derived by the first author [Nonlinear Analysis, TM&A 28 (1997), 1741–1750]. The purpose of this paper is to discuss the uniqueness and properties of unbounded positive solutions and investigate some further structures of the positive solutions of Eq. (1.1)
Structure of the sets of regular and singular radial solutions for a semilinear elliptic equation
No full textAbstractThis paper is concerned with the structure of the set of radially symmetric solutions for the equationΔu+f(u)=0onRn⧹{0},with n>2. Here the nonlinear term f is assumed to be a smooth function of u that is positive for u>0 and is equal to 0 for u⩽0. Then any radial solution u=u(r),r=|x|, of the equation is shown to be classified into one of several types according to its behavior as r→0 and r→∞. Under the assumption that f is supercritical for small u>0 and is subcritical for large u>0, we clarify the entire structure of the set of solutions of various types. The Pohozaev identity plays a crucial role in the investigation of the structure
Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions
Get PDFWe are concerned with the uniqueness of weak solution to the spatially
homogeneous Landau equation with Coulomb interactions under the assumption that
the solution is bounded in the space for some
. The proof uses a weighted Poincar\'e-Sobolev inequality recently
introduced in \cite{GG18}
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Positive Singular Solutions to a Nonlinear Elliptic Equation on the Unit Sphere (Qualitative theory of ordinary differential equations in real domains)
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