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**Search for:**nonlinear-boundary-value-problems

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#### An existence-uniqueness theorem for a class of boundary value problems

, Article Fixed Point Theory ; Volume 13, Issue 2 , 2012 , Pages 589-592 ; 15835022 (ISSN) ; Pournaki, M. R ; Razani, A ; Sharif University of Technology
2012

Abstract

In this paper the solutions of a two-endpoint boundary value problem is studied and under suitable assumptions the existence and uniqueness of a solution is proved. As a consequence, a condition to guarantee the existence of at least one periodic solution for a class of Liénard equations is presented

#### Erratum to "On the existence of periodic solutions for a class of generalized forced Liénard equations" [Appl. Math. Lett. 20 (3) (2007) 248-254]

, Article Applied Mathematics Letters ; Volume 21, Issue 8 , August , 2008 , Page 880 ; 08939659 (ISSN) ; Razani, A ; Sharif University of Technology
2008

Abstract

In this work the second-order generalized forced Li ́enard equationx′′+(f(x)+k(x)x′)x′+g(x)=p(t)is considered and anew condition for guaranteeing the existence of at least one periodic solution for this equation is given

#### Instability of nanocantilever arrays in electrostatic and van der waals interactions

, Article Journal of Physics D: Applied Physics ; Volume 42, Issue 22 , 2009 ; 00223727 (ISSN) ; Alasty, A ; Sharif University of Technology
2009

Abstract

The structural instability of an array of cantilevers, each of which interacts with two neighbouring beams through electrostatic and van der Waals forces, is studied. Distributed and lumped parameter modelling of the array result in a set of coupled nonlinear boundary value problems and a set of coupled nonlinear equations, respectively. These coupled nonlinear systems are solved numerically for different numbers of beams in the array to obtain the pull-in parameters. The pull-in parameters converge to constant values with an increase in the number of beams in the array. These constants, which are important in the design of cantilever arrays, are compared for the distributed and lumped...

#### Prediction of the penetrated rust into the microcracks of concrete caused by reinforcement corrosion

, Article Applied Mathematical Modelling ; Volume 35, Issue 5 , 2011 , Pages 2529-2543 ; 0307904X (ISSN) ; Shodja, H. M ; Sharif University of Technology
2011

Abstract

Consider a steel-rust-concrete composite consisting of a circular cylindrical concrete cover and a coaxial uniformly corroding steel reinforcement. Prediction of the amount of rust penetrated into the microcracks of concrete cover from a set of data measured at the surface of the concrete is of particular interest. The steel is assumed to be linear isotropic and rust follows a power law stress-strain relation. For the concrete, anisotropic behavior and post-cracking softening model is employed. The formulations lead to a nonlinear boundary value problem which is solved analytically. A key parameter β, defined as the ratio of the volume of corrosion products inside the cracks to the volume of...

#### Combined action of Casimir and electrostatic forces on nanocantilever arrays

, Article Acta Mechanica ; Volume 212, Issue 3-4 , July , 2010 , Pages 305-317 ; 00015970 (ISSN) ; Alasty, A ; Sharif University of Technology
2010

Abstract

Cantilever arrays with nearest-neighbor interactions are considered to obtain the pull-in parameters. The interactions between the neighboring beams are a combination of the Casimir force and the electrostatic force with the first-order fringing field correction. A set of coupled nonlinear boundary value problems and a set of coupled nonlinear equations arise in the distributed and lumped parameter modeling of the array, respectively. The models are simulated numerically to obtain the pull-in parameters of the arrays with different number of beams. The pull-in parameters of large arrays converge to constant values, which are independent of the number of beams in the array. The constants...

#### Analytical solutions for the static instability of nano-switches under the effect of casimir force and electrostatic actuation

, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings, 13 November 2009 through 19 November 2009 ; Volume 12, Issue PART A , 2010 , Pages 63-69 ; 9780791843857 (ISBN) ; Moeenfard, H ; Ahmadian, M. T ; Sharif University of Technology
Abstract

This paper deals with the problem of static instability of nano switches under the effect of Casimir force and electrostatic actuation. The nonlinear fringing field effect has been accounted for in the model. Using a Galerkin decomposition method and considering only one mode, the nonlinear boundary value problem describing the static behavior of nano-switch, is reduced to a nonlinear boundary value ordinary differential equation which is solved using the homotopy perturbation method (HPM). In order to ensure the precision of the results, the number of included terms in the perturbation expansion has been investigated. Results have been compared with numerical results and also with...