In this paper we use the method of upper and lower solutions combined with degree theoretic techniques to prove the existence of multiple positive solutions to semipositone superlinear systems of the form −∆u = g1(x, u, v) −∆v = g2(x, u, v) on a smooth, bounded domain Ω ⊂ R with Dirichlet boundary conditions, under suitable conditions on g1 and g2. Our techniques apply generally to subcritical,...

Let B0(s, t) be a Brownian pillow with continuous sample paths, and let h, u : [0, 1] 2 → R be two measurable functions. In this paper we derive upper and lower bounds for the boundary non-crossing probability ψ(u;h) := P{B0(s, t) + h(s, t) ≤ u(s, t), ∀s, t ∈ [0, 1]}. Further we investigate the asymptotic behaviour of ψ(u; γh) with γ tending to ∞, and solve a related minimisation problem.

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

In this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient te...

ANTONIO ALARC´ON ABSTRACT. In this paper we construct complete minimal surfaces with boundary in R 3 of arbitrary finite topology. For any arbitrary finite topological type we find a compact Riemann surface M, an open domain M ⊂ M with the fixed topological type, and a conformal complete minimal immersion X : M → R 3 which can be extended to a continuous map X : M → R 3 , such that X |∂M is an ...

Abstract We consider a linearized fluid-structure interaction problem, namely the flow of an incompressible viscous fluid in half space $${\mathbb {R}}^n_+$$ R + n such that on lower boundary function h satisfying undamped K...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

where the functions f , g : [0, 1]× R→ R and h : [0, 1]× R→ R\{0} satisfy some special assumptions that will be given in detail in Section 3. Boundary value problems arise in a variety of applied mathematics and physics areas (refer to [1, 2] etc.). Some boundary value problems of ordinary equations may be turned into (1.1)-(1.2). For example, in the design of bridge, denote u(t) by the displac...

We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants. For a right rectangular prism and a large class of topologies, we derive upper bounds by introducing test configurations constructed from local conformal solut...