In this paper we give a sufficient and necessary condition under which a continuous measure (whose values belong to, the extended half-line (0,+∞) defined on a class of sets closed under the formation of intersection...In this paper we give a sufficient and necessary condition under which a continuous measure (whose values belong to, the extended half-line (0,+∞) defined on a class of sets closed under the formation of intersection can be extended to a smallest monotone class containing this class, and we also give a condition under which there exists a unique extension. In addition, we give a method by means of which a continuous measure on a monotone class can be extended again.展开更多
This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),...This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),where βi∈ R,m-3 ∑i=1 β i=1,0 < η 1 < η 2 < ··· < ηm-3 < 1,m-3 ∑i=1 βiηi=1,0 < ξ < 1.An existence theorem is obtained by using the extension of Mawhin's continuation theorem.Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin's continuation theorem,our method is new.展开更多
In this paper,we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields.These theorems provide close relationship among range inclusion,majorization and factorization for ...In this paper,we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields.These theorems provide close relationship among range inclusion,majorization and factorization for bounded linear operators.It is found that these results depend strongly on a continuous extension property,which is always true in the classical archimedean case,but may fail to hold for the non-archimedean setting.Several counterexamples are given to show that our results are sharp in some sense.展开更多
文摘In this paper we give a sufficient and necessary condition under which a continuous measure (whose values belong to, the extended half-line (0,+∞) defined on a class of sets closed under the formation of intersection can be extended to a smallest monotone class containing this class, and we also give a condition under which there exists a unique extension. In addition, we give a method by means of which a continuous measure on a monotone class can be extended again.
文摘This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),where βi∈ R,m-3 ∑i=1 β i=1,0 < η 1 < η 2 < ··· < ηm-3 < 1,m-3 ∑i=1 βiηi=1,0 < ξ < 1.An existence theorem is obtained by using the extension of Mawhin's continuation theorem.Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin's continuation theorem,our method is new.
基金supported by National Natural Science Foundation of China(Grant Nos.10831007,60821091 and 60974035)National Basic Research Program of China(Grant No.2011CB808002),Independent Innovation Foundation of Shandong Universitythe project MTM2008-03541 of the Spanish Ministry of Science and Innovation
文摘In this paper,we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields.These theorems provide close relationship among range inclusion,majorization and factorization for bounded linear operators.It is found that these results depend strongly on a continuous extension property,which is always true in the classical archimedean case,but may fail to hold for the non-archimedean setting.Several counterexamples are given to show that our results are sharp in some sense.
