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
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.
