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We consider a semilinear elliptic system with both concave–convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.
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We improve some results on the existence and multiplicity of solutions for the (p_1(x), . . . , p_n(x))-biharmonic system. Our main results are new. Our approach is based on general variational principle and the theory of the vari...
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We improve some results on the existence and multiplicity of solutions for the (p_1(x), . . . , p_n(x))-biharmonic system. Our main results are new. Our approach is based on general variational principle and the theory of the variable exponent Sobolev spaces.
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For a bounded, open set ?∈R~N and depending on λ>0, we study the multiplicity of solutions of where M(x) is a symmetric, bounded, and elliptic matrix and 0
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This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: where α ∈ (1/2,1], a(x) ∈ L~∞[0, T] with a_0 = essinf_(x∈[0,7]a(x) > 0, D_~(T-)~α and D_(0+)~α ...
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This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: where α ∈ (1/2,1], a(x) ∈ L~∞[0, T] with a_0 = essinf_(x∈[0,7]a(x) > 0, D_~(T-)~α and D_(0+)~α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f : [0,T] × R → R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.
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Classical and generalized Newton's methods as applied to the calculation of simple and multiple roots of a nonlinear equation are examined. For these two methods the algorithms are developed for determining the root's order during...
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Classical and generalized Newton's methods as applied to the calculation of simple and multiple roots of a nonlinear equation are examined. For these two methods the algorithms are developed for determining the root's order during calculations. For multiple roots the algorithm that accelerates convergence is developed. It also allows us to determine a root even to a high order with high accuracy. The details of all algorithms are examined carefully. Based on that, the program that surpasses well-known standard programs in accuracy and reliability is developed.
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There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by usi...
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There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Most of the model updating methods used in structural dynamics are for linear systems. However, in real life applications most of the structures have nonlinearities, which restrict us applying model updating techniques available for linear structures, unless they work in linear range. Well-established frequency response function (FRF) based model updating methods would easily be extended to a nonlinear system if the FRFs of the underlying linear system (linear FRFs) could be experimentally measured. When frictional type of nonlinearity co-exists with other types of nonlinearities, it is not possible to obtain linear FRFs experimentally by using low level forcing. In this study a method (named as Pseudo Receptance Difference (PRD) method) is presented to obtain linear FRFs of a nonlinear structure having multiple nonlinearities including friction type of nonlinearity. PRD method, calculates linear FRFs of a nonlinear structure by using FRFs measured at various forcing levels, and simultaneously identifies all nonlinearities in the system. Then, any model updating method can be used to update the linear part of the mathematical model. In this present work, PRD method is used to predict the linear FRFs from measured nonlinear FRFs, and the inverse eigensensitivity method is employed to update the linear finite element (FE) model of the nonlinear structure. The proposed method is validated with different case studies using nonlinear lumped single-degree of freedom system, as well as a continuous system. Finally, a real nonlinear T-beam test structure is used to show the application and the accuracy of the proposed method. The accuracy of the updated nonlinear model of the test structure is demonstrated by comparing the calculated and measured nonlinear FRFs of the test structure at several different forcing levels.
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The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearitie...
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The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.
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An initial-boundary value problem for strongly nonlinear generalized Boussinesq equation is studied. We show the exponential growth of solution with L_p-norm for negative or positive initial energy by constructing differential inequalities.
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The process characteristics and control strategy of a high-purity IPA reactive distillation column were investigated. A robust nominal operation was found by maintaining an excess of propylene feed to the column and recycling the ...
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The process characteristics and control strategy of a high-purity IPA reactive distillation column were investigated. A robust nominal operation was found by maintaining an excess of propylene feed to the column and recycling the unreacted propylene to the feed instead of the top stage. Stage temperature and propylene composition with one-to-one relationship with reboiler duty and propylene feed are selected as controlled variables for maintaining bottom purity and feed ratio in the presence of possible measurement bias respectively. High nonlinearity between selected input-output pair was reduced by using variable transformation. Dynamic simulations demonstrated that such a control scheme with nonlinear transformed variable was capable of providing much superior control performance than the one using natural variable. (C) 2005 Elsevier Ltd. All rights reserved.
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This paper deals with boundary value problems whose nonlinear part involves periodic functions and such that the linear part has a one-dimensional solution space. We shall study the existence and multiplicity of solutions using va...
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This paper deals with boundary value problems whose nonlinear part involves periodic functions and such that the linear part has a one-dimensional solution space. We shall study the existence and multiplicity of solutions using various methods of Nonlinear Analysis such as the Lyapunov-Schmidt reduction and methods of critical point theory. The proofs are based on some general results on the oscillation and asymptotic behavior of certain parametric integrals. (c) 2005 Elsevier Inc. All rights reserved.
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