Boundary Value Problems - Latest Articles
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The latest research articles published by Boundary Value Problems2014-04-17T13:10:33ZAsymptotic profile of solutions to the semilinear beam equationIn this paper, we investigate the initial value problem for the semilinear beam equation. Under a small condition on the initial value, we prove the global existence and optimal decay estimate of solutions. Moreover, we show that as time tends to infinity, the solution is asymptotic to a diffusion wave, which is given explicitly in terms of the solution of parabolic equation.MSC:
35L30, 35L75.
http://www.boundaryvalueproblems.com/content/2014/1/84
Yunpeng ZhangYanling LiBoundary Value Problems 2014, null:842014-04-17T13:10:33Zdoi:10.1186/1687-2770-2014-84/content/figures/1687-2770-2014-84-toc.gifBoundary Value Problems1687-2770${item.volume}842014-04-17T13:10:33ZXMLOscillation criteria for neutral second-order half-linear differential equations with applications to Euler type equationsWe study the second-order neutral delay half-linear differential equation [r(t)Φ(z′(t))]′+q(t)Φ(x(σ(t)))=0, where Φ(t)=|t|α−1t, α≥1 and z(t)=x(t)+p(t)x(τ(t)). We use the method of Riccati type substitution and derive oscillation criteria for this equation. By an example of the neutral Euler type equation we show that the obtained results are sharp and improve the results of previous authors. Among others, we improve the results of Sun et al. (Abstr. Appl. Anal. 2012:819342, 2012) and discuss also the case when σ∘τ≠τ∘σ.MSC:
34K11, 34K40.
http://www.boundaryvalueproblems.com/content/2014/1/83
Simona Fi¿narováRobert Ma¿íkBoundary Value Problems 2014, null:832014-04-10T11:25:46Zdoi:10.1186/1687-2770-2014-83/content/figures/1687-2770-2014-83-toc.gifBoundary Value Problems1687-2770${item.volume}832014-04-10T11:25:46ZXMLThe solvability of nonhomogeneous boundary value problems with ¿ -Laplacian operatorWe treat the nonhomogeneous boundary value problems with ϕ-Laplacian operator (ϕ(u′(t)))′=−f(t,u(t),u′(t)), t∈(0,T), u(0)=A, ϕ(u′(T))=τu(T)+∑i=1kτiu(ζi), where ϕ:(−a,a)→(−b,b) (0<a,b≤+∞) is an increasing homeomorphism such that ϕ(0)=0, τ,τi∈R, ζi∈(0,T), i=1,2,…,k, A≥0, and f:[0,T]×R×R→R is continuous. We will show that even if some of the τ and τi are negative, the boundary value problem with singular ϕ-Laplacian operator is always solvable, and the problem with a bounded ϕ-Laplacian operator has at least one positive solution.
http://www.boundaryvalueproblems.com/content/2014/1/82
Sha-Sha ChenZhi-Hong MaBoundary Value Problems 2014, null:822014-04-10T09:35:18Zdoi:10.1186/1687-2770-2014-82/content/figures/1687-2770-2014-82-toc.gifBoundary Value Problems1687-2770${item.volume}822014-04-10T09:35:18ZXMLRiemann boundary value problem for H-2-monogenic function in Hermitian Clifford analysisHermitian Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions of two Hermitian Dirac operators. Using a circulant matrix approach, we will study the R0 Riemann type problems in Hermitian Clifford analysis. We prove a mean value formula for the Hermitian monogenic function. We obtain a Liouville-type theorem and a maximum module for the function above. Applying the Plemelj formula, integral representation formulas, and a Liouville-type theorem, we prove that the R0 Riemann type problems for Hermitian monogenic and Hermitian-2-monogenic functions are solvable. Explicit representation formulas of the solutions are also given.
http://www.boundaryvalueproblems.com/content/2014/1/81
Longfei GuZunwei FuBoundary Value Problems 2014, null:812014-04-09T12:57:23Zdoi:10.1186/1687-2770-2014-81/content/figures/1687-2770-2014-81-toc.gifBoundary Value Problems1687-2770${item.volume}812014-04-09T12:57:23ZXMLPositive solutions for elastic beam equations with nonlinear boundary conditions and a parameterThis paper is concerned with the existence, nonexistence, and uniqueness of convex monotone positive solutions of elastic beam equations with a parameter λ. The boundary conditions mean that the beam is fixed at one end and attached to a bearing device or freed at the other end. By using fixed point theorem of cone expansion, we show that there exists λ∗≥λ∗>0 such that the beam equation has at least two, one, and no positive solutions for 0<λ≤λ∗, λ∗<λ≤λ∗ and λ>λ∗, respectively; furthermore, by using cone theory we establish some uniqueness criteria for positive solutions for the beam and show that such solution xλ depends continuously on the parameter λ. In particular, we give an estimate for critical value of parameter λ.MSC:
34B18, 34B15.
http://www.boundaryvalueproblems.com/content/2014/1/80
Wenxia WangYanping ZhengHui YangJunxia WangBoundary Value Problems 2014, null:802014-04-09T11:10:52Zdoi:10.1186/1687-2770-2014-80/content/figures/1687-2770-2014-80-toc.gifBoundary Value Problems1687-2770${item.volume}802014-04-09T11:10:52ZXMLA BDDC algorithm for the mortar-type rotated $Q_{1}$ FEM for elliptic problems with discontinuous coefficientsIn this paper, we propose a BDDC preconditioner for the mortar-type rotated Q1 finite element method for second order elliptic partial differential equations with piecewise but discontinuous coefficients. We construct an auxiliary discrete space and build our algorithm on an equivalent auxiliary problem, and we present the BDDC preconditioner based on this constructed discrete space. Meanwhile, in the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasi-optimal convergence behavior, i.e., the condition number of the preconditioned problem is independent of the jumps of the coefficients, and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.MSC:
65N55, 65N30.
http://www.boundaryvalueproblems.com/content/2014/1/79
Yaqin JiangJinru ChenBoundary Value Problems 2014, null:792014-04-03T10:05:34Zdoi:10.1186/1687-2770-2014-79/content/figures/1687-2770-2014-79-toc.gifBoundary Value Problems1687-2770${item.volume}792014-04-03T10:05:34ZXML Symmetric positive solutions of higher-order boundary value problemsWe study the higher-order boundary value problems. The existence of symmetric positive solutions of the problem is discussed. Our results extend some recent work in the literature. The analysis of this paper mainly relies on the monotone iterative technique.MSC:
34B15, 34B18.
http://www.boundaryvalueproblems.com/content/2014/1/78
Yan LuoBoundary Value Problems 2014, null:782014-04-03T10:00:30Zdoi:10.1186/1687-2770-2014-78/content/figures/1687-2770-2014-78-toc.gifBoundary Value Problems1687-2770${item.volume}782014-04-03T10:00:30ZXMLExistence of nonnegative nontrivial periodic solutions to a doubly degenerate parabolic equation with variable exponentThe authors investigate a degenerate parabolic equation with delay and nonlocal term, which describes slow diffusive processes in physics or biology. The existence of a nonnegative nontrivial periodic solution is obtained through the use of the Leray-Schauder degree method.MSC:
35D05, 35K55.
http://www.boundaryvalueproblems.com/content/2014/1/77
Zhongqing LiWenjie GaoBoundary Value Problems 2014, null:772014-04-02T13:55:12Zdoi:10.1186/1687-2770-2014-77/content/figures/1687-2770-2014-77-toc.gifBoundary Value Problems1687-2770${item.volume}772014-04-02T13:55:12ZXMLr -Modified Crank-Nicholson difference scheme for fractional parabolic PDEThe second order of accuracy stable difference scheme for the numerical solution of the mixed problem for the fractional parabolic equation are presented using by r-modified Crank-Nicholson difference scheme. Stability estimate for the solution of this difference scheme is obtained. A procedure of modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional parabolic partial differential equations. Numerical results for this scheme and the Crank-Nicholson scheme are compared in test examples.
http://www.boundaryvalueproblems.com/content/2014/1/76
Allaberen AshyralyevZafer CakirBoundary Value Problems 2014, null:762014-03-31T17:05:38Zdoi:10.1186/1687-2770-2014-76/content/figures/1687-2770-2014-76-toc.gifBoundary Value Problems1687-2770${item.volume}762014-03-31T17:05:38ZXMLUniform attractors for non-autonomous suspension bridge-type equationsWe discuss the long-time dynamical behavior of the non-autonomous suspension bridge-type equation, where the nonlinearity g(u,t) is translation compact and the time-dependent external forces h(x,t) only satisfy Condition (C∗) instead of being translation compact. By applying some new results and the energy estimate technique, the existence of uniform attractors is obtained. The result improves and extends some known results.MSC:
34Q35, 35B40, 35B41.
http://www.boundaryvalueproblems.com/content/2014/1/75
Xuan WangLu YangQiaozhen MaBoundary Value Problems 2014, null:752014-03-28T13:07:43Zdoi:10.1186/1687-2770-2014-75/content/figures/1687-2770-2014-75-toc.gifBoundary Value Problems1687-2770${item.volume}752014-03-28T13:07:43ZXML