In this paper,the authors obtain the existence of one-signed periodic solutions of the first-order functional difference equation ？u（n） = a（n）u（n）-λb（n）f（u（n-τ（n）））,n ∈ Z by using global bifurcation ...In this paper,the authors obtain the existence of one-signed periodic solutions of the first-order functional difference equation ？u（n） = a（n）u（n）-λb（n）f（u（n-τ（n）））,n ∈ Z by using global bifurcation techniques,where a,b：Z → [0,∞） are T-periodic functions with ∑T n=1 a（n） 〉 0,∑T n=1 b（n） 〉 0;τ：Z → Z is T-periodic function,λ 〉 0 is a parameter;f ∈ C（R,R） and there exist two constants s2 〈 0 〈 s1 such that f（s2） = f（0） = f（s1） = 0,f（s） 〉 0 for s ∈（0,s1） ∪（s1,∞）,and f（s） 〈 0 for s ∈（-∞,s2） ∪（s2,0）.展开更多
This paper concerns the exact multiplicity of one-sign solutions of a class of quasilinear elliptic eigenvalue problems with asymptotical nonlinearity at 0 and ∞. The proofs of our main results are based upon bifurca...This paper concerns the exact multiplicity of one-sign solutions of a class of quasilinear elliptic eigenvalue problems with asymptotical nonlinearity at 0 and ∞. The proofs of our main results are based upon bifurcation techniques and stability analysis.展开更多
In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the ...In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the bifurcation result,we determine the intervals ofλfor the existence,nonexistence,and exact multiplicity of one-sign solutions for this problem.展开更多
In this paper,we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity.As applications of the above res...In this paper,we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity.As applications of the above result,we shall prove the existence of one-sign solutions to the following problem{−div(√∇v 1−|∇v|^(2))=α(x)v^(+)+β(x)v^(−)+λa(x)f(v),in B_(R)(0),v(x)=0,on∂B_(R)(0),whereλ≠=0 is a parameter,R is a positive constant and BR(0)={x∈RN:|x|<R}is the standard open ball in the Euclidean space RN(N≥1)which is centered at the origin and has radius R.v^(+)=max{v,0},v−=−min{v,0},a(x)∈C(BR(0),(0,+∞)),α(x),β(x)∈C(BR(0)),a(x),α(x)andβ(x)are radially symmetric with respect to x;f∈C(R,R),sf(s)>0 for s≠=0,and f_(0)∈[0,∞],where f0=lim_(|s|)→0 f(s)/s.We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.We also study the asymptotic behaviors of positive radial solutions asλ→+∞.展开更多
In this work,we study the existence of one-sign solutions for the following problem:{-Δu=λa(x)f(u),in R^(N)u(x)→0,as|x|→+∞,where N≥3,λis a real parameter and a∈C^(α)_(loc)(R^(N),R)for someα∈(0,1)is a weight...In this work,we study the existence of one-sign solutions for the following problem:{-Δu=λa(x)f(u),in R^(N)u(x)→0,as|x|→+∞,where N≥3,λis a real parameter and a∈C^(α)_(loc)(R^(N),R)for someα∈(0,1)is a weighted function,f:R→R is a Hölder continuous function with exponentαsuch that f(s)s>0 for any s≠O.We determine the intervals ofλfor the existence,exact multiplicity of onesign solutions for this problem.We use bifurcation techniques and the approximation of connected components to prove our main results.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1162618811671322+2 种基金11501451)the Natural Science Foundation of Gansu Province(Grant No.1606RJYA232)the Young Teachers’ Scientific Research Capability Upgrading Project of Northwest Normal University(Grant No.NWNU-LKQN-15-16)
文摘In this paper,the authors obtain the existence of one-signed periodic solutions of the first-order functional difference equation ？u（n） = a（n）u（n）-λb（n）f（u（n-τ（n）））,n ∈ Z by using global bifurcation techniques,where a,b：Z → [0,∞） are T-periodic functions with ∑T n=1 a（n） 〉 0,∑T n=1 b（n） 〉 0;τ：Z → Z is T-periodic function,λ 〉 0 is a parameter;f ∈ C（R,R） and there exist two constants s2 〈 0 〈 s1 such that f（s2） = f（0） = f（s1） = 0,f（s） 〉 0 for s ∈（0,s1） ∪（s1,∞）,and f（s） 〈 0 for s ∈（-∞,s2） ∪（s2,0）.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1126105211101335)
文摘This paper concerns the exact multiplicity of one-sign solutions of a class of quasilinear elliptic eigenvalue problems with asymptotical nonlinearity at 0 and ∞. The proofs of our main results are based upon bifurcation techniques and stability analysis.
基金Supported by the National Natural Science Foundation of China(11561038)。
文摘In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the bifurcation result,we determine the intervals ofλfor the existence,nonexistence,and exact multiplicity of one-sign solutions for this problem.
基金Supported by the`Kaiwu'Innovation Team Support Project of Lanzhou Institute of Technology(2018KW-03),the NSFC(11561038).
文摘In this paper,we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity.As applications of the above result,we shall prove the existence of one-sign solutions to the following problem{−div(√∇v 1−|∇v|^(2))=α(x)v^(+)+β(x)v^(−)+λa(x)f(v),in B_(R)(0),v(x)=0,on∂B_(R)(0),whereλ≠=0 is a parameter,R is a positive constant and BR(0)={x∈RN:|x|<R}is the standard open ball in the Euclidean space RN(N≥1)which is centered at the origin and has radius R.v^(+)=max{v,0},v−=−min{v,0},a(x)∈C(BR(0),(0,+∞)),α(x),β(x)∈C(BR(0)),a(x),α(x)andβ(x)are radially symmetric with respect to x;f∈C(R,R),sf(s)>0 for s≠=0,and f_(0)∈[0,∞],where f0=lim_(|s|)→0 f(s)/s.We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.We also study the asymptotic behaviors of positive radial solutions asλ→+∞.
基金supported by the Key Scientific Research Project of Guangdong University of Science and Technology(No.GKY-2024KYZDK-18)NSFC(No.11561038).
文摘In this work,we study the existence of one-sign solutions for the following problem:{-Δu=λa(x)f(u),in R^(N)u(x)→0,as|x|→+∞,where N≥3,λis a real parameter and a∈C^(α)_(loc)(R^(N),R)for someα∈(0,1)is a weighted function,f:R→R is a Hölder continuous function with exponentαsuch that f(s)s>0 for any s≠O.We determine the intervals ofλfor the existence,exact multiplicity of onesign solutions for this problem.We use bifurcation techniques and the approximation of connected components to prove our main results.
