In this paper we prove that, given a compact four dimensional smooth Riemannian manifold (M, g) with smooth boundary there exists a metric conformal to g with constant T -curvature, zero Q-curvature and zero mean curvature under generic and conformally invariant assumptions. The problem amounts to solving a fourth order nonlinear elliptic boundary value problem (BVP) with boundary conditions gi...

We consider linear systems with coefficient matrices having the ABD or the Bordered ABD (BABD) structures. These systems arise in the discretization of BVPs for ordinary and partial differential equations with separated and non-separated boundary conditions, respectively. We describe the cyclic reduction algorithm for the solution of BABD linear systems which allowed us to write the codes BABDC...

This paper investigates the existence of positive solutions for the following high-order nonlinear fractional differential boundary value problem (BVP, for short)  Dα 0+u(t) + f(t, v(t)) = 0, t ∈ (0, 1), Dα 0+v(t) + g(t, u(t)) = 0, t ∈ (0, 1), u(j)(0) = v(j)(0) = 0, 0 ≤ j ≤ n− 1, j 6= 1, u′(1) = λ ∫ 1 0 u(t)dt, v′(1) = λ ∫ 1 0 v(t)dt, where n − 1 < α ≤ n, n ≥ 3, 0 ≤ λ < 2, Dα 0+ is the ...

Investigation of positive solutions of multipoint second-order ordinary boundary value problems, initiated by Il’in and Moiseev [1, 2], has been extensively addressed by many authors, for instance, see [3–6]. Multipoint problems refer to a different family of boundary conditions in the study of disconjugacy theory [7]. Recently, Eloe and Ahmad [8] addressed a nonlinear nth-order BVP with nonloc...

We consider numerical methods for the computation and continuation of the three generic secondaryperiodicsolution bifurcationsin autonomousordinarydiierentialequations(ODEs), namely the fold, the period-doubling (or ip) bifurcation, and the torus (or Neimark-Sacker) bifur-cation. In the fold and ip cases we append one scalar equation to the standard periodic boundary value problem (BVP) that de...

We study a bifurcation problem for the equation ∆u+λu+ g(λ, u) = 0 on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. Here λ ∈ R is the bifurcation parameter, and g is a small perturbation. Under certain assumptions concerning an eigenfunction u0 corresponding to an eigenvalue λ0 of the ...

Every applied mathematician has used separation of variables. For a given boundary value problem (BVP) in two dimensions, the starting point of this powerful method is the separation of the given PDE into two ODEs. If the spectral analysis of either of these ODEs yields an appropriate transform pair, i.e., a transform consistent with the given boundary conditions, then the given BVP can be redu...

Abstract Funding Acknowledgements Type of funding sources: None. Introduction Despite optimal medical treatment, the 5-years mortality and HF readmission rate was 75.3% 48.5%, respectively. The current guidelines recommended cardiac resynchronization therapy (CRT) by implanting biventricular pacing (BVP) for specific group patients with reduced ejection fraction (HFrEF) in order to reduce risk ...

The technique of space invariant embedding, applied to a second order boundary value problem defined in a cylindrical domain, gives rise to a system of uncoupled first order initial value problems that includes a nonlinear Riccati equation on a unbounded functional operator. We present a method to justify this equation that uses a parabolic regularization of the original problem.

In this paper, the authors examine sufficient condition for the uniqueness of positive solutions of singular Strum-Liouville boundary value problems ( ) ( ) ( ) ) ( , , ) , ( , ) ( ) ( ) ( BVP E u u f t u u in BC u u (ψ θ θ α θ β θ ′ ′ ′ + ′ = − ′ 0 1 2