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1.
We present some results on the existence and multiplicity of solutions for boundary value problems involving equations of the type −Δu=f(x,u)+λg(x,u), where Δ is the Laplacian operator, λ is a real parameter and , are two Carathéodory functions having no growth conditions with respect to the second variable. The approach is variational and mainly based on a critical point theorem by B. Ricceri. 相似文献
2.
Nonradial large solutions of sublinear elliptic problems 总被引:1,自引:0,他引:1
Khalifa El Mabrouk Wolfhard Hansen 《Journal of Mathematical Analysis and Applications》2007,330(2):1025-1041
Let p be a nonnegative locally bounded function on , N3, and 0<γ<1. Assuming that the oscillation sup|x|=rp(x)−inf|x|=rp(x) tends to zero as r→∞ at a specified rate, it is shown that the equation Δu=p(x)uγ admits a positive solution in satisfying lim|x|→∞u(x)=∞ if and only if 相似文献
3.
We investigate the partial linear spaces, fully embedded in an affine space with the property that for every antiflag {p,L}, the number of lines through p intersecting L is either 0,α, or q. Besides some general results we prove a complete classification of those geometries fully embedded in an affine plane of order q and of the connected geometries with 1<α<q, fully embedded in . 相似文献
4.
Given a strictly convex, smooth, and bounded domain Ω in we establish the existence of a negative convex solution in with zero boundary value to the singular Monge–Ampère equation det(D2u)=p(x)g(−u). An associated Dirichlet problem will be employed to provide a necessary and sufficient condition for the solvability of the singular boundary value problem. Estimates of solutions will also be given and regularity of solutions will be deduced from the estimates. 相似文献
5.
Norman L. Johnson Giuseppe Marino Olga Polverino Rocco Trombetti 《Finite Fields and Their Applications》2008,14(2):456-469
In [G. Marino, O. Polverino, R. Trombetti, On -linear sets of PG(3,q3) and semifields, J. Combin. Theory Ser. A 114 (5) (2007) 769–788] it has been proven that there exist six non-isotopic families (i=0,…,5) of semifields of order q6 with left nucleus and center , according to the different geometric configurations of the associated -linear sets. In this paper we first prove that any semifield of order q6 with left nucleus , right and middle nuclei and center is isotopic to a cyclic semifield. Then, we focus on the family by proving that it can be partitioned into three further non-isotopic families: , , and we show that any semifield of order q6 with left nucleus , right and middle nuclei and center belongs to the family . 相似文献
6.
We prove the relative asymptotic behavior for the ratio of two sequences of multiple orthogonal polynomials with respect to the Nikishin systems of measures. The first Nikishin system is such that for each k, σk has a constant sign on its compact support consisting of an interval , on which almost everywhere, and a discrete set without accumulation points in . If denotes the smallest interval containing , we assume that Δk∩Δk+1=0/, k=1,…,m−1. The second Nikishin system is a perturbation of the first by means of rational functions rk, k=1,…,m, whose zeros and poles lie in . 相似文献
7.
Jackson’s theorem is established in a new kind of holomorphic function space Qμ related to measures in any starlike circular domain in . Particularly, the result covers many spaces including BMOA, Qp, QK, and F(p,q,s) spaces in the unit ball of . Moreover, we construct integral operators which give pointwise estimates for the gradient of the difference in terms of the gradient on the boundary. The gradient estimates are independent of the measures in question and give rise to Jackson’s theorem. 相似文献
8.
On an extremal problem of Selberg 总被引:1,自引:1,他引:0
We consider the minimum value mp of the product under the conditions that and . This problem stems from estimation of the Selberg integral appeared in the study of integral-valued entire functions [A. Selberg, Über einen Satz von A. Gelfond, Arch. Math. Naturvid. 44 (1941) 159–170]. We give upper and lower estimates of mp : . This, in particular, slightly improves the earlier lower estimate given by Selberg: logmp>p·0.31654924…. 相似文献
9.
The aim of this paper is to discuss the positive solutions of the p-Laplace problem
−div(|u|p−2u)+g(u)|u|p=λuq,