# Author

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• (European Mathematical Society, 2017)
• (2018-04)
In this note, we discuss the isolatedness, simplicity and nodal estimate for the first eigenvalue of fractional Laplacian of Kirchhoff type. This work is motivated by the recent works on the fractional eigenvalues.
• (Texas State University, Department of Mathematics, 2011-11)
By the method of monotone iteration and Schauder fixed point theorem, we prove the existence of non-negative solutions to the system = for λ sufficiently small, where is a bounded domain in RN with smooth boundary ∂Ω and ...
In this paper we study the existence of solutions to the following semilinear elliptic problem TeX where TeX is an open bounded subset of TeX and TeX The special feature of this problem is that it has singularity at the ...
• (Mathematical Society of the Republic of China, 2017-04)
• (Institute of Mathematics and Informatics, 2020-06)
• (The Mathematical Society of the Republic China, 2013-01)
The goal of this paper is to show a generalization to Sturm--Picone theorem for a pair of second-order nonlinear differential equations (p_1(t)x'(t))'+ q_1(t)f_{1}(x(t))=0. (p_2(t)y'(t))'+ q_2(t)f_{2}(y(t))=0, ...
• (Elsevier, 2012-06)
In this note, we show the existence of a global positive solution for a class of first-order delay differential equations: x′(t)+a1(t)x(t)+a2(t)x(t−h(t))=0.x′(t)+a1(t)x(t)+a2(t)x(t−h(t))=0. Turn MathJax on In this study, ...
• (Cambridge University Press, 2020-01)
• (American Institute of Mathematical Sciences (AIMS), 2013-05)
In this article, we prove the existence of multiple weak solutions to N-Laplace equation -δNu - μ g(x) ( x log R x )N u N-2u = γf(x; u) in ω. u = 0 on ω using Bonanno's three critical point theorem.
• (Elsevier, 2013-06)
The purpose of this note is to show a generalization to Picone’s identity in a nonlinear framework. The classical Picone’s identity turns out to be a particular case of our result. We show, as an application of our results, ...
• (Wiley, 2020-04)
We establish the existence of nonnegative weak solutions to nonlinear reaction�diffusion system with cross?diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that ...
• (De Gruyter, 2014-05)
• (European Mathematical Society (EMS), 2018-10)
In this note, we establish Leighton's variational lemma for fractional Laplace equations. We use the classical techniques to establish this variational lemma. We also point out several questions concerning the zeros of the ...
• (Springer Berlin Heidelberg, 2016-08)
In this note, we establish a Caccioppoli-type inequality for biharmonic operators. We employ Picone’s identity for biharmonic operators to establish Caccioppoli-type inequality.
• (De Gruyter, 2013-10)
In this note, we prove a stability theorem for a class of quasilinear elliptic equations -δp u = a(x)u-f(x,u) in Ω, u=0 on δΩ, where δp u= div(/∇uu/ p-2∇u) 2 ≤ p < p < ∞ ,Ω ⊂ &RdblN is an open, smooth and bounded subset. ...
• (Taylor & Francis, 2013-06)
In this note, we discuss an eigenvalue problem involving Hardy's potential with homogeneous Dirichlet boundary condition in a smooth bounded domain. We show that the problem possesses a continuous family of eigenvalues.
• (InforMath Publishing Group, 2011-03)
In this paper, we obtain some oscillation criteria for the second-order linear differential equation x″(t)+p(t)x(t)=0.
• (Springer, 2016-04)
In this paper, we establish a nonlinear analogue of Picone’s identity for biharmonic operators on Heisenberg group. As an applications of Picone’s identity, we obtain Hardy-Rellich type inequality, Morse index, Caccioppoli ...
• (Spriger, 2017-08)
In this paper, we establish the existence of a positive solution to {−M+λ,Λ(D2u)=μk(x)f(u)uα−ηh(x)uqu=0in Ωon ∂Ω, {−Mλ,Λ+(D2u)=μk(x)f(u)uα−ηh(x)uqin Ωu=0on ∂Ω, where ΩΩ is a smooth bounded domain in Rn, n≥1.Rn, n≥1. ...