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91.
Sturmian comparison theory for half‐linear and nonlinear differential equations via Picone identity 下载免费PDF全文
Abdullah Özbekler 《Mathematical Methods in the Applied Sciences》2017,40(8):3100-3110
In this paper, Sturmian comparison theory is developed for the pair of second‐order differential equations; first of which is the nonlinear differential equations of the form (1) and the second is the half‐linear differential equations (2) where Φα (s ) = |s |α ? 1s and α 1 > ? > α m > β > α m + 1 > ? > α n > 0. Under the assumption that the solution of 2 has two consecutive zeros, we obtain Sturm–Picone type and Leighton type comparison theorems for 1 by employing the new nonlinear version of Picone formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for 1 . Examples are given to illustrate the relevance of the results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
92.
Heng Li Yongzhi Xu Jian‐Rong Zhou 《Mathematical Methods in the Applied Sciences》2017,40(10):3566-3579
Ductal carcinoma in situ – a special cancer – is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
93.
《Macromolecular bioscience》2017,17(8)
Tissue expansion is used by plastic/reconstructive surgeons to grow additional skin/tissue for replacing or repairing lost or damaged soft tissues. Recently, hydrogels have been widely used for tissue expansion applications. Herein, a self‐inflating tissue expander blend composition from three different molecular weights (2, 6, and 10 kDa) of poly (ethylene glycol) diacrylate (PEGDA) hydrogel with tunable mechanical and swelling properties is presented. The in vitro results demonstrate that, of the eight studied compositions, P6 (PEGDA 6 kDa:10 kDa (50:50)) and P8 (PEGDA 6 kDa:10 kDa (35:65)) formulations provide a balance of mechanical property and swelling capability suitable for tissue expansion. Furthermore, these expanders can be compressed up to 60% of their original height and can be loaded and unloaded cyclically at least ten times with no permanent deformation. The in vivo results indicate that these two engineered blend compositions are capable to generate a swelling pressure sufficient to dilate the surrounding tissue while retaining their original shape. The histological analyses reveal the formation of fibrous capsule at the interface between the implant and the subcutaneous tissue with no signs of inflammation. Ultimately, controlling the PEGDA chain length shows potential for the development of self‐inflating tissue expanders with tunable mechanical and swelling properties.
94.
Abstract : Second‐order nonlinear optical (NLO) dendrimers with a special topological structure were regarded as the most promising candidates for practical applications in the field of optoelectronic materials. Dendronized hyperbranched polymers (DHPs), a new type of polymers with dendritic structures, proposed and named by us recently, demonstrated interesting properties and some advantages over other polymers. Some of our work concerning these two types of polymers are presented herein, especially focusing on the design idea and structure–property relationship. To enhance their comprehensive NLO performance, dendrimers were designed and synthesized by adjusting their isolation mode, increasing the number of the dendritic generation, modifying their topological structure, introducing isolation chromophores, and utilizing the Ar‐ArF self‐assembly effect. To make full use of the advantages of both the structural integrity of dendrimers and the convenient one‐pot synthesis of hyperbranched polymers, DHPs were explored by utilizing low‐generation dendrons as big monomers to construct hyperbranched polymers. These selected works could provide valuable information to deeply understand the relationship between the structure and properties of functional polymers with dendritic structures, but not only limited to the NLO ones, and might contribute much to the further development of functional polymers with rational design. 相似文献
95.
96.
In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method. 相似文献
97.
In this paper, the nonlinear iterative methods, which are different from the classical algorithms, to solve inverse problems are presented. Our methods by denoting some parameters and some properties of the algorithm in both noise and noiseless cases are studied. Finally, the convergence of the sequence generated by the algorithm without noise is discussed. 相似文献
98.
Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains 下载免费PDF全文
Elyas Shivanian Ahmad Jafarabadi 《Numerical Methods for Partial Differential Equations》2017,33(4):1043-1069
In present work, a kind of spectral meshless radial point interpolation (SMRPI) technique is applied to the time fractional nonlinear Schrödinger equation in regular and irregular domains. The applied approach is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. It is proved the scheme is unconditionally stable with respect to the time variable in and also convergent by the order of convergence , . In the current work, the thin plate spline are used as the basis functions and to eliminate the nonlinearity, a simple predictor‐corrector (P‐C) scheme is performed. It is shown that the SMRPI solution, as a complex function, is suitable one for the time fractional nonlinear Schrödinger equation. The results of numerical experiments are compared to analytical solutions to confirm the reliable treatment of these stable solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1043–1069, 2017 相似文献
99.
Positive ground state of coupled systems of Schrödinger equations in
involving critical exponential growth 下载免费PDF全文
João Marcos do Ó José Carlos de Albuquerque 《Mathematical Methods in the Applied Sciences》2017,40(18):6864-6879
In this paper, we study the existence of a positive ground state solution to the following coupled system of nonlinear Schrödinger equations: where the nonlinearities f1(x,s) and f2(x,s) are superlinear at infinity and have exponential critical growth of the Trudinger‐Moser type. The potentials V1(x) and V2(x) are nonnegative and satisfy a condition involving the coupling term λ(x), namely, λ(x)2<δ2V1(x)V2(x) for some 0<δ<1. For this purpose, we use the minimization technique over the Nehari manifold and strong maximum principle to get a positive ground state solution. Moreover, by using a bootstrap argument and Lq‐estimates, we get regularity and asymptotic behavior. 相似文献
100.
Existence and limit behavior of prescribed L2‐norm solutions for Schrödinger‐Poisson‐Slater systems in
下载免费PDF全文
In this paper, we study constraint minimizers of the following L 2?critical minimization problem: where E (u ) is the Schrödinger‐Poisson‐Slater functional and N denotes the mass of the particles in the Schrödinger‐Poisson‐Slater system. We prove that e (N ) admits minimizers for and, however, no minimizers for N >N ?, where Q (x ) is the unique positive solution of in . Some results on the existence and nonexistence of minimizers for e (N ?) are also established. Further, when e (N ?) does not admit minimizers, the limit behavior of minimizers as N ↗N ? is also analyzed rigorously. 相似文献