Proceedings of the Royal Society of Edinburgh Section A: Mathematics

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On singular quasi-monotone (p, q)-Laplacian systems
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 142 Số 3 - Trang 585-594 - 2012
Said El Manouni, Kanishka Perera, R. Shivaji
We combine the sub- and supersolution method and perturbation arguments to obtain positive solutions of singular quasi-monotone (p, q)-Laplacian systems.
Existence of a positive solution for a singular system
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 140 Số 2 - Trang 435-447 - 2010
Marcelo Montenegro, António Suárez
We show the existence and non-existence of positive solutions to a system of singular elliptic equations with the Dirichlet boundary condition.
A Lane–Emden system with singular data
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 141 Số 6 - Trang 1279-1294 - 2011
Marius Ghergu
We study the elliptic system −Δu = δ(x)−avp in Ω, −Δv = δ(x)−buq in Ω, subject to homogeneous Dirichlet boundary conditions. Here, Ω ⊂ ℝN, N ≥ 1, is a smooth and bounded domain, δ(x) = dist(x, ∂Ω), a, b ≥ 0 and p, q ∈ ℝ satisfy pq > −1. The existence, non-existence and uniqueness of solutions are investigated in terms of a, b, p and q.
Local existence and blow-up criterion for the Boussinesq equations
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 127 Số 5 - Trang 935-946 - 1997
Dongho Chae, Hee-Seok Nam
SynopsisIn this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove global existence of smooth solutions... hiện toàn bộ
Using Melnikov's method to solve Silnikov's problems
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 116 Số 3-4 - Trang 295-325 - 1990
Xiao-Biao Lin
SynopsisA function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite. Examples include generalisations of Silnikov's main theorems and a retreatment o... hiện toàn bộ
Symmetry for elliptic equations in a half-space without strong maximum principle
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 134 Số 2 - Trang 259-269 - 2004
Yihong Du, Zongming Guo
For a wide class of nonlinearities f(u) satisfying but not necessarily Lipschitz continuous, we study the quasi-linear equation where T = {x = (x1, x2, …, xN) ∈ RN: x1 > 0} with N ≥ 2. By using a new approach based on the weak maximum principle, we show that any positive solution on T must be a function of x1 only. Under our assumptions, the strong maximum principle does not hold in general and th... hiện toàn bộ
A deletion-contraction algorithm for the characteristic polynomial of a multigraph
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 105 Số 1 - Trang 153-160 - 1987
Peter Rowlinson
SynopsisThe characteristic polynomial of a finite multigraph G is expressed in terms of characteristic polynomials oflocal modifications of G. The resulting formula is used to investigate the largest eigenvalues of certain theta graphs.
The bond-based peridynamic system with Dirichlet-type volume constraint
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 144 Số 1 - Trang 161-186 - 2014
Tadele Mengesha, Qiang Du
In this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and non-local peridynamic models, to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on ... hiện toàn bộ
The effective equilibrium law for a highly heterogeneous elastic periodic medium
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 143 Số 3 - Trang 507-561 - 2013
Hamid Charef, Ali Sili
We study the homogenization of the linearized system of elasticity standing for the equilibrium equation of a highly periodic heterogeneous elastic medium submitted to small deformations and made of two different materials: a very rigid material located in a set Fε (ε being the size of the period of the medium) of vertical fibres surrounded by a soft elastic material localized in the set Mε. The r... hiện toàn bộ
A relationship between the periodic and the Dirichlet BVPs of singular differential equations
Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 128 Số 5 - Trang 1099-1114 - 1998
Meirong Zhang
In this paper, a relationship between the periodic and the Dirichlet boundary value problems for second-order ordinary differential equations with singularities is established. This relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations. Using this relationship, we give in this paper an existence result of positive period... hiện toàn bộ
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