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We investigate the Lipschitz structure of ℓp and Lp for 0<p<1 as quasi-Banach spaces and as metric spaces (with the metric induced by the p-norm) and show that they are not Lipschitz isomorphic. We prove that the -space L0 is not uniformly homeomorphic to any other Lp space, that the Lp spaces for 0<p<1 embed isometrically into one another, and reduce the problem of the uniform equivalence amongst Lp spaces to their Lipschitz equivalence as metric spaces. 相似文献
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Consider Robin problem involving the p(x)-Laplacian on a smooth bounded domain Ω as follows Applying the sub-supersolution method and the variational method, under appropriate assumptions on f, we prove that there exists λ*>0 such that the problem has at least two positive solutions if λ(0,λ*), has at least one positive solution if λ=λ*<+∞ and has no positive solution if λ>λ*. To prove the results, we prove a norm on W1,p(x)(Ω) without the part of ||Lp(x)(Ω) which is equivalent to usual one and establish a special strong comparison principle for Robin problem. 相似文献
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In this paper we study the rates of A-statistical convergence of sequences of positive linear operators mapping the weighted space Cρ1 into the weighted space Bρ2. 相似文献
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An n-ary operation Q:Σn→Σ is called an n-ary quasigroup of order |Σ| if in the relation x0=Q(x1,…,xn) knowledge of any n elements of x0,…,xn uniquely specifies the remaining one. Q is permutably reducible if Q(x1,…,xn)=P(R(xσ(1),…,xσ(k)),xσ(k+1),…,xσ(n)) where P and R are (n-k+1)-ary and k-ary quasigroups, σ is a permutation, and 1<k<n. An m-ary quasigroup S is called a retract of Q if it can be obtained from Q or one of its inverses by fixing n-m>0 arguments. We prove that if the maximum arity of a permutably irreducible retract of an n-ary quasigroup Q belongs to {3,…,n-3}, then Q is permutably reducible. 相似文献
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In this paper, we study the existence of periodic solutions for a fourth-order p-Laplacian differential equation with a deviating argument as follows:
[φp(u″(t))]″+f(u″(t))+g(u(t−τ(t)))=e(t).