1,720,998 research outputs found
The well-posedness of the integral equations for thin wire antennas
No full textIn this paper the author shows that the Pocklington and Hallen integral equations for the current induced on a thin wire by an incident harmonic electromagnetic field are well-posed. It is also shown that the solutions must lie in certain Sobolev spaces of absolutely continuous functions. © 1992 Oxford University Press.</p
The Hausdorff Dimension of Sets Arising from Diophantine Approximation with a General Error Function
No full textLetm,nbe positive integers and let?:Zn?R be a non-negative function. LetW(m, n; ?) be the setX?Rmn:?j=1nxijqj<?(q), 1=i=m, for infinitely manyq?Zn.The Hausdorff dimension ofW(m, n; ?) is obtained for arbitrary non-negative functions?, with no monotonicity assumptions. © 1998 Academic Press.</p
Simultaneous Diophantine approximation on manifolds and Hausdorff dimension
No full textLet M be an m-dimensional, Ck manifold in Rn, for any k, m, n ? ?, and for any t> 0 let Lt(M)={x?M : ?qx?<q-t for infinitely many q??}, where, for x?R, ?x? min{ x - i :i?Z}, and for x=(x1,?,xn)???n, ?X? = max{?x1pr,?,?xn?}. In this paper it will be shown that for any Ck manifold M there exist Ck manifolds Mz, Mp arbitrarily 'Ck-close' to M with the property that, for all sufficiently large t, dimLt(Mz)=0, dim Lt(Mp)>0. This result shows that the non-zero curvature conditions which have been successfully used to tackle other aspects of the theory of Diophantine approximation on manifolds are unable to distinguish between these two cases when we look at simultaneous Diophantine approximation. © 2002 Elsevier Science (USA). All rights reserved.</p
The Fucik spectrum of general Sturm-Liouville problems
No full textConsider the boundary value problem-(pu')'+qu=au+-ßu-,in(0, p),c00u(0)+c01u'(0)=0,c10u(p)+c11u'(p)=0, where u±=max{±u, 0}. The set of points (a, ß)?R2 for which this problem has a non-trivial solution is called the Fucik spectrum. When p=1, q=0, and either Dirichlet or periodic boundary conditions are imposed, the Fucik spectrum is known explicitly and consists of a countable collection of curves, with certain geometric properties. In this paper we show that similar properties hold for the general problem above, and also for a further generalization of the Fucik spectrum. We also discuss some spectral type properties of a positively homogeneous, "half-linear" problem and use these results to consider the solvability of a nonlinear problem with jumping nonlinearities. © 2000 Academic Press.</p
Non-resonance Conditions for Semilinear Sturm-Liouville Problems with Jumping Non-linearities
No full textWe consider the Sturm-Liouville boundary value problem-(p(x)u'(x))'+q(x)u(x)=f(x, u(x))+h(x), x?(0, p),c00u(0)+c01u'(0)=0, c10u(p)+c11u'(p)=0,where p?C1([0, p]), q?C0([0, p]), with p(x)>0, x?[0, p], c2i0+c2i1>0, i=0, 1, h?L2(0, p), and f:[0, p]×R?R is a Carathéodory function. We assume that the rate of growth of f(x, ?) is at most linear as ??8, but the asymptotic behaviour may be different as ??±8, so the non-linearity is termed "jumping." Conditions for existence of solutions of this problem are usually expressed in terms of "non-resonance" with respect to the standard Fucík spectrum. In this paper we give conditions for both existence and non-existence of solutions in terms of a slightly different idea of the spectrum. These conditions extend the usual Fucík spectrum conditions. © 2001 Academic Press.</p
Eigenvalue criteria for existence of positive solutions Of second-order, multi-point, p-laplacian boundary value problems
No full textIn this paper we consider the existence and uniqueness of positive solutions of the multi-point boundary value problem (1) - (Øp(u?)?+(a+g(x,u,u?)Øp(u) =0, a.e. on (-1,1), (2) u(±1)=Si=1 ±ai±u(? i±) where p>1, Øp(s) p-2s, se R,m± = 1 are integer, and ?i±?(-1,1), ai± > 0, i=1 ,?,m±, Si=1m±ai± Also a ? L1(-1,1) and g: [-1,1]× R 2?R is Carath´eodory, with (3) g(x,0,0)=0, x ?[-1,1]. Our criteria for existence of positive solutions of (1), (2) will be expressed in terms of the asymptotic behaviour of g(x, s, t), as s ? 8, and the principal eigenvalues of the multi-point boundary value problem consisting of the equation (4) -Ø(u?)?+aØp(u)= ?Øp(u), on (-1,1) Copyright © 2010 Juliusz Schauder Center for Nonlinear Studies.</p
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
p-Laplacian problems with jumping nonlinearities
No full textWe consider the p-Laplacian boundary value problem{A formula is presented}{A formula is presented} where p > 1 is a fixed number, f{symbol}p ( s ) = | s |p - 2 s, s ? R, and for each j = 0, 1, | cj 0 | + | cj 1 | > 0. The function f : [ 0, 1 ] × R2 ? R is a Carathéodory function satisfying, for ( x, s, t ) ? [ 0, 1 ] × R2,{A formula is presented} where ?±, ?± ? L1 ( 0, 1 ), and E has the form E ( x, s, t ) = ? ( x ) e ( | s | + | t | ), with ? ? L1 ( 0, 1 ), ? {greater than or slanted equal to} 0, e {greater than or slanted equal to} 0 and limr ? 8 e ( r ) r1 - p = 0. This condition allows the nonlinearity in (1) to behave differently as u ? ± 8. Such a nonlinearity is often termed jumping. Related to (1), (2) is the problem{A formula is presented} together with (2), where a, b ? L1 ( 0, 1 ), ? ? R, and u± ( x ) = max { ± u ( x ), 0 } for x ? [ 0, 1 ]. This problem is 'positively-homogeneous' and jumping. Values of ? for which (2), (3) has a nontrivial solution u will be called half-eigenvalues, while the corresponding solutions u will be called half-eigenfunctions. We show that a sequence of half-eigenvalues exists, the corresponding half-eigenfunctions having certain nodal properties, and we obtain certain spectral and degree theoretic properties of the set of half-eigenvalues. These properties lead to existence and nonexistence results for the problem (1), (2). We also consider a related bifurcation problem, and obtain a global bifurcation result similar to the well-known Rabinowitz global bifurcation theorem. This then leads to a multiplicity result for (1), (2). When the functions a and b are constant the set of half-eigenvalues is closely related to the 'Fucík spectrum' of the problem, and equivalent solvability results are obtained using the two approaches. However, when a and b are not constant the half-eigenvalue approach yields stronger results. © 2005 Elsevier Inc. All rights reserved.</p
Nonresonance conditions for generalised φ-Laplacian problems with jumping nonlinearities
No full textWe consider the boundary value problem(0.1)- ? (x, u (x), u' (x))' = f (x, u (x), u' (x)), a.e. x ? (0, 1),(0.2)c00 u (0) = c01 u' (0), c10 u (1) = c11 u' (1), where | cj 0 | + | cj 1 | > 0, for each j = 0, 1, and ?, f : [0, 1] × R2 ? R are Carathéodory functions, with suitable additional properties. The differential operator generated by the left-hand side of (0.1), together with the boundary conditions (0.2), is a generalisation of the usual p-Laplacian, and also of the so-called f{symbol}-Laplacian (which corresponds to ? (x, s, t) = f{symbol} (t), with f{symbol} an odd, increasing homeomorphism). For the p-Laplacian problem (and more particularly, the semilinear case p = 2), 'nonresonance conditions' which ensure the solvability of the problem (0.1), (0.2), have been obtained in terms of either eigenvalues (for non-jumping f) or the Fucík spectrum or half-eigenvalues (for jumping f) of the p-Laplacian. In this paper, under suitable growth conditions on ? and f, we extend these conditions to the general problem (0.1), (0.2). © 2009 Elsevier Inc. All rights reserved.</p
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