244 research outputs found
Art, Biography, Sexuality: Patrick Procktor and Keith Vaughan
No full textThis critical review forms a reflection on the research published within the following publications:
Patrick Procktor: Art and Life (Unicorn Press, 2010)
Keith Vaughan: The Mature Oils 1946-1977, (Sansom & Co., 2012)
The research is on two artists, Patrick Procktor (1936-2003), and Keith Vaughan (1912-1977). The monograph on Procktor – previously one of the least documented of the generation of artists who came to prominence in London in the Sixties – positions him in a history of art from which he had been notably absent. The research on Vaughan asserts a new reading of his work, one that is both deeper and more nuanced in its analysis of the ways in which personal experience and sexuality are encoded autobiographically within his work. Crucially, in both artists biography and work are symbiotically linked; the research therefore examines the links between life and art.
Revisionary in intent, the work examines trajectories of experience of gay British (or rather, English) artists in the twentieth century, artists who sought to express themselves and forge careers within the constraints of a heteronormative society, albeit one in which attitudes to sexuality were undergoing change. As gay men, both were constrained by the social mores of their times, and each used painting as a means to affirm personal and sexual identities. A key research interest is in the ways in which sexuality and persona are reflected in critical responses to the artist’s work: in Vaughan, Procktor and other gay male artists of the period. The writing on both Procktor and Vaughan examines the relationship between their personal and professional/artistic lives, framed within a broader socio-political and art historical context. It asserts the place of biography as a means to understand and form new readings of the work. The work adds substantially to the literature and wider discourse on post-war British painting and social history
Infinitely many solutions of superlinear fourth order boundary value problems
No full textAbstract. We consider the boundary value problem u(4)(x) = g(u(x)) + p(x, u(0)(x),..., u(3)(x)), x ∈ (0, 1)
Bifurcation from zero or infinity in Sturm-Liouville problems which are not linearizable
No full textWe consider the nonlinear Sturm-Liouville problem[formula][formula]whereai,biare real numbers with ai+bi0,i=0,1, ? is a real parameter, and the functionspandaare strictly positive on [0,p]. Suppose that the nonlinearityhsatisfies a condition of the form[formula]as either (?,?)?0 or (?,?)?8, for some constantsM0,M1. Then we show that there exist global continua of nontrivial solutions (?,u) bifurcating fromu=0 or "u=8," respectively. These global continua have properties similar to those of the continua found in Rabonowitz' well-known global bifurcation theorem. © 1998 Academic Press.</p
Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions
No full textWe consider the eigenvalue problem for the equation on , together with general Sturm-Liouville-type, multi-point boundary conditions at . We show that the basic spectral properties of this problem are similar to those of the standard Sturm-Liouville problem with separated boundary conditions. In particular, for each integer there exists a unique, simple eigenvalue whose eigenfunctions have 'oscillation count' equal to k
Simple bifurcation and global curves of solutions of p-Laplacian problems with radial symmetry
No full textGlobal stability, or instability, of positive equilibria of p-Laplacian boundary value problems with p-convex nonlinearities
Full text linkWe consider the parabolic, initial value problem
vt = Δp(v) + λg(x, v)φp(v), in Ω x (0,∞), v = 0, in ∂Ω x (0,∞), (IVP) v = v0 > 0, in Ω x {0}, where Ω is a bounded domain in RN , for some integer N > 1, with smooth boundary ∂Ω, φp(s) := |s|p−1 sgn s , s ∈ R , and Δp denotes the p -Laplacian, with p > max{2,N} , v0 ∈ C0(Ω) , and λ > 0 . The function g : Ω x [0,∞) → (0,∞) is C0 and, for each x ∈ Ω , the function g(x, ·) : [0,∞) → (0,∞) is Lipschitz continuous and strictly increasing.
Clearly, (IVP) has the trivial solution v ≡ 0 , for all λ > 0 . In addition, there exists 0 < λmin(g) < λmax(g) such that:
• if λ ∈/ (λmin(g),λmax(g)) then (IVP) has no non-trivial, positive
equilibrium;
• there exists a closed, connected set of positive equilibria bifurcating
from (λmax(g), 0) and ‘meeting infinity’ at λ = λmin(g) .
We prove the following results on the positive solutions of (IVP):
• if 0 < λ < λmin(g) then the trivial solution is globally asymptotically
stable;
• if λmin(g) < λ < λmax(g) then the trivial solution is locally asymptotically stable and all non-trivial, positive equilibria are unstable;
• if λmax(g) < λ then any non-trivial solution blows up in finite
time
Global bifurcation for 'th order boundary value problems and infinitely many solutions of superlinear problems
No full textWe consider the boundary value problem Lu(x) = p(x)u(x) + g(x, u(0)(x),...,u(2m-1)(x))u(x), x?(0,p), (*) where (i) L is a 2mth order, self-adjoint, disconjugate ordinary differential operator on [0, p], together with separated boundary conditions at 0 and p; (ii) p is continuous and p = 0 on [0, p], while p ? 0 on any interval in [0, p]; (iii) g: [0, p] × R2m ?R is continuous and there exist increasing functions ?u, ?l : [0, 8) ? [0, 8) such that with limt?8 ?l(t) = 8 (the non-linear term in (*) is superlinear as u(x) ? 8). We obtain a global bifurcation result for a related bifurcation problem. We then use this to obtain infinitely many solutions of (*) having specified nodal properties. © 2002 Elsevier Science (USA). All rights reserved.</p
Convergence of Galerkin method solutions of the integral equation for thin wire antennas
No full textIn this paper we consider the Pocklington integro-differential equation for the current induced on a straight, thin wire by an incident harmonic electromagnetic field. We show that this problem is well posed in suitable fractional order Sobolev spaces and obtain a coercive or Carding type inequality for the associated operator. Combining this coercive inequality with a standard abstract formulation of the Galerkin method we obtain rigorous convergence results for Galerkin type numerical solutions of Pocklington's equation, and we demonstrate that certain convergence rates hold for these methods. © J.C. Baltzer AG, Science Publishers.</p
Global asymptotic stability of bifurcating, positive equilibria of p-Laplacian boundary value problems with p-concave nonlinearities
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