We consider the m-point boundary value problem consisting of the equation −u′′ = f(u), on (0, 1), where f : R → R is C1, with f(0) = 0, together with the boundary conditions u(0) = 0, u(1) = m−2 X

We consider the boundary value problem u(x) = g(u(x)) + p(x, u(x), . . . , u(x)), x ∈ (0, 1), u(0) = u(1) = u(0) = u(1) = 0, where: (i) g : R → R is continuous and satisfies lim|ξ|→∞ g(ξ)/ξ = ∞ (g is… (More)

We consider the boundary value problem Lu(x) = p(x)u(x) + g(x, u(x), . . . , u(2m−1)(x))u(x), x ∈ (0, π), (1) where: (i) L is a 2m’th order, self-adjoint, disconjugate ordinary differential operator… (More)

Let T ⊂ R be a bounded time-scale, with a = inf T, b = sup T. We consider the weighted, linear, eigenvalue problem −(pu ) (t) + q(t)u (t) = λw(t)u (t), t ∈ Tκ , c00u(a) + c01u (a) = 0, c10u ( ρ(b) )… (More)

We reconsider the basic formulation of second-order, two-point, Sturm-Liouville-type boundary value problems on time scales. Although this topic has received extensive attention in recent years, we… (More)

In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := −[pu∇]∆ + qu, on an arbitrary, bounded time-scale T, for suitable functions p, q, together… (More)

We consider the structure of the solution set of a nonlinear SturmLiouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of… (More)

In 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… (More)

Let (r); r = 1; 2; : : : be a positive decreasing sequence such that P 1 r=1 (r) k diverges. Using a powerful variance argument due to W. M. Schmidt, an asymptotic formula is obtained for the number… (More)