Boundary Value Problems - Latest Articles
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The latest research articles published by Boundary Value Problems2015-03-31T00:00:00Z Multiplicity of solutions for fractional Schrödinger equations with perturbation In this paper, we investigate a class of fractional Schrödinger equations with perturbation. By using the mountain pass theorem and Ekeland’s variational principle, we see that such equations possess two solutions. Recent results in the literature are generalized and significantly improved.MSC: 34B15.
http://www.boundaryvalueproblems.com/content/2015/1/56
Liu YangBoundary Value Problems 2015, null:562015-03-31T00:00:00Zdoi:10.1186/s13661-015-0317-5/content/figures/s13661-015-0317-5-toc.gifBoundary Value Problems1687-2770${item.volume}562015-03-31T00:00:00ZXML An iterative regularization method for an abstract ill-posed biparabolic problem In this paper, we are concerned with the problem of approximating a solution of an ill-posed biparabolic problem in the abstract setting. In order to overcome the instability of the original problem, we propose a regularizing strategy based on the Kozlov-Maz’ya iteration method. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution.MSC: 47A52, 65J22.
http://www.boundaryvalueproblems.com/content/2015/1/55
Abdelghani LakhdariNadjib BoussetilaBoundary Value Problems 2015, null:552015-03-28T00:00:00Zdoi:10.1186/s13661-015-0318-4/content/figures/s13661-015-0318-4-toc.gifBoundary Value Problems1687-2770${item.volume}552015-03-28T00:00:00ZXML Exact and asymptotic analysis of waves generated by sea-floor disturbances on a sloping beach A two-dimensional problem of small amplitude waves generated by some sea-bottom disturbance is studied on a sloping beach. The exact analytical solution for the wave height is provided, and with a periodic ground motion the asymptotic analysis of the waves is shown to exist for all time even in the vicinity of the shoreline. The novelty of this work lies in solving the corresponding Fredholm integral equation of the first kind and also to provide a uniform asymptotic estimate of the wave integral in the unsteady state involving both pole and saddle points for which Van der Waerden’s method is used. Within the framework of linear irrotational theory, explicit integral solutions of waves and their asymptotic and/or numerical computations presented here aim to provide an equivalent mathematical understanding to all such wave propagation which can be modelled in two dimensions at the open sea.
http://www.boundaryvalueproblems.com/content/2015/1/54
Arghya BandyopadhyayMaria Otero-EspinarBoundary Value Problems 2015, null:542015-03-26T12:00:00Zdoi:10.1186/s13661-015-0315-7/content/figures/s13661-015-0315-7-toc.gifBoundary Value Problems1687-2770${item.volume}542015-03-26T12:00:00ZXML Infinite first order differential systems with nonlocal initial conditions We discuss the solvability of an infinite system of first order ordinary differential equations on the half line, subject to nonlocal initial conditions. The main result states that if the nonlinearities possess a suitable ‘sub-linear’ growth then the system has at least one solution. The approach relies on the application, in a suitable Fréchet space, of the classical Schauder-Tychonoff fixed point theorem. We show that, as a special case, our approach covers the case of a system of a finite number of differential equations. An illustrative example of an application is also provided.MSC: 34A12, 34A34, 47H30.
http://www.boundaryvalueproblems.com/content/2015/1/53
Gennaro InfantePetru JebeleanFadila MadjidiBoundary Value Problems 2015, null:532015-03-21T12:00:00Zdoi:10.1186/s13661-015-0314-8/content/figures/s13661-015-0314-8-toc.gifBoundary Value Problems1687-2770${item.volume}532015-03-21T12:00:00ZXML Periodic and subharmonic solutions for a class of the second-order Hamiltonian systems with impulsive effects This paper is concerned with the existence of periodic and subharmonic solutions for a class of the second-order impulsive Hamiltonian systems. It employs the linking theorem.
http://www.boundaryvalueproblems.com/content/2015/1/52
Jingli XieJianli LiZhiguo LuoBoundary Value Problems 2015, null:522015-03-21T00:00:00Zdoi:10.1186/s13661-015-0313-9/content/figures/s13661-015-0313-9-toc.gifBoundary Value Problems1687-2770${item.volume}522015-03-21T00:00:00ZXML Approximation of the inverse elliptic problem with mixed boundary value conditions and overdetermination In the present study, the inverse problem for a multidimensional elliptic equation with mixed boundary conditions and overdetermination is considered. The first and second orders of accuracy in t and the second order of accuracy in space variables for the approximate solution of this inverse problem are constructed. Stability, almost coercive stability, and coercive stability estimates for the solution of these difference schemes are established. For the two-dimensional inverse problems with mixed boundary value conditions, numerical results are presented in test examples.MSC: 35N25, 39A14, 39A30, 65J22.
http://www.boundaryvalueproblems.com/content/2015/1/51
Charyyar AshyralyyevMutlu DedeturkBoundary Value Problems 2015, null:512015-03-17T12:00:00Zdoi:10.1186/s13661-015-0312-x/content/figures/s13661-015-0312-x-toc.gifBoundary Value Problems1687-2770${item.volume}512015-03-17T12:00:00ZXML Optimal control for evolutionary imperfect transmission problems We study the optimal control problem of a second order linear evolution equation defined in two-component composites with ε-periodic disconnected inclusions of size ε in presence of a jump of the solution on the interface that varies according to a parameter γ. In particular here the case
γ
<
1
is analyzed. The optimal control theory, introduced by Lions (Optimal Control of System Governed by Partial Differential Equations, 1971), leads us to characterize the control as the solution of a set of equations, called optimality conditions. The main result of this paper proves that the optimal control of the ε-problem, which is the unique minimum point of a quadratic cost functional
J
ε
, converges to the optimal control of the homogenized problem with respect to a suitable limit cost functional
J
∞
. The main difficulties are to find the appropriate limit functional for the control of the homogenized system and to identify the limit of the controls.MSC: 49J20, 35B37, 35B27.
http://www.boundaryvalueproblems.com/content/2015/1/50
Luisa FaellaCarmen PerugiaBoundary Value Problems 2015, null:502015-03-17T12:00:00Zdoi:10.1186/s13661-015-0310-z/content/figures/s13661-015-0310-z-toc.gifBoundary Value Problems1687-2770${item.volume}502015-03-17T12:00:00ZXMLExistence of multi-valued solutions with asymptotic behavior of parabolic Monge-Ampère equationIn this paper, we extend the results of multi-valued solutions of elliptic Monge-Ampère equation to parabolic Monge-Ampère equation. We use the Perron method to prove the existence of multi-valued solutions with asymptotic behavior at infinity of parabolic Monge-Ampère equation. Moreover, we prove that the multi-valued solution is continuous in the whole space.MSC: 35K96, 35B40.
http://www.boundaryvalueproblems.com/content/2015/1/49
Limei DaiBoundary Value Problems 2015, null:492015-03-04T00:00:00Zdoi:10.1186/s13661-015-0307-7/content/figures/s13661-015-0307-7-toc.gifBoundary Value Problems1687-2770${item.volume}492015-03-04T00:00:00ZXMLAn application of variational approach to a class of damped vibration problems with impulsive effects on time scalesIn this paper, we present a new approach via variational methods and critical point theory to obtain the existence and multiplicity of solutions to a class of damped vibration problems with impulsive effects on time scales. By establishing a proper variational set, two existence results and two multiplicity results are obtained. Finally, one example is presented to illustrate the feasibility and effectiveness of our results.
http://www.boundaryvalueproblems.com/content/2015/1/48
Jianwen ZhouYanning WangYongkun LiBoundary Value Problems 2015, null:482015-03-04T00:00:00Zdoi:10.1186/s13661-015-0305-9/content/figures/s13661-015-0305-9-toc.gifBoundary Value Problems1687-2770${item.volume}482015-03-04T00:00:00ZXMLGlobal attractors of the 3 He- 4 He system in H¿ spacesIn this paper, the existence of a global attractor for the 3He-4He system is investigated. By using an iteration procedure, combining with the classical existence theorem of global attractors, we prove that this system possesses a global attractor, which attracts any bounded set of
H
α
in
H
α
-norm.MSC: 35B40, 35Q56.
http://www.boundaryvalueproblems.com/content/2015/1/46
Dongming YanBoundary Value Problems 2015, null:462015-03-03T12:00:00Zdoi:10.1186/s13661-015-0308-6/content/figures/s13661-015-0308-6-toc.gifBoundary Value Problems1687-2770${item.volume}462015-03-03T12:00:00ZXML