Existence results for impulsive fractional differential equations with pp-Laplacian via variational methods

summary:This paper presents several sufficient conditions for the existence of at least one classical solution to impulsive fractional differential equations with a $p$-Laplacian and Dirichlet boundary conditions. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented

Differential quadrature method (DQM) for studying initial imperfection effects and pre- and post-buckling vibration of plates

The effects of initial geometric imperfection and pre- and post-buckling deformations on vibration of isotropic rectangular plates under uniaxial compressive in-plane load have been studied. The differential equations of plate motions, using the Mindlin theory and Von-Karman stress-strain relations for large deformations, were extracted. The solution of nonlinear differential equations was assumed as the summation of dynamic and static solutions. Due to a large static plate deflection as compared with its vibration amplitude, the differential equations were solved in two steps. First, the static equations were solved using the differential quadrature method and the arc-length strategy. Next, considering small vibration amplitude about the deformed shape and eliminating nonlinear terms, the natural frequencies were extracted using the differential quadrature method. The results for different initial geometric imperfection and different boundary conditions reflect the impact of the mentioned factors on the natural frequencies of plates

Three solutions for second-order boundary-value problems with variable exponents

This paper presents several sufficient conditions for the existence of at least three weak solutions of a nonhomogeneous Neumann problem for an ordinary differential equation with p(x)-Laplacian operator. The technical approach is variational, based on a theorem of Bonanno and Candito. An example is also given

Crack detection in beams using Hilbert-Huang transform

This study presents a non-destructive method for detecting location and depth of crack in beams. The method utilizes Hilbert-Huang Transform (HHT) as a time-series analysis technique. Crack is considered to be open and has been modeled by rotational spring. First, the natural frequencies of the cracked beam are calculated using Timoshenko’s beam theory. Then by using the vibration signals corresponding to the beam, experimental natural frequencies are calculated by Fast Fourier Transform (FFT) and HHT. Finally, with the help of Artificial Bee Colony, the location and depth of the crack are predicted by minimization of an objective function. The objective function is constructed by the weighted sum of the squared errors between the theoretical and experimental natural frequencies of the cracked beams. To investigate the feasibility of proposed method, cracks in different locations and depths are introduced in steel beams and crack parameters are predicted. The results show that both the location and depth of the crack can be predicted well through the proposed method. Moreover, by using the experimental natural frequencies obtained by HHT method, cracks (especially small depth) can be detected with a better precision than FFT method

Three solutions for second-order boundary-value problems with variable exponents

This paper presents several sufficient conditions for the existence of at least three weak solutions of a nonhomogeneous Neumann problem for an ordinary differential equation with $p(x)$-Laplacian operator. The technical approach is variational, based on a theorem of Bonanno and Candito. An example is also give

Multiple solutions for a Kirchhoff-type second-order impulsive differential equation on the half-line

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Generalized Yamabe equations on Riemannian manifolds and applications to Emden-Fowler problems

In this paper, we establish the existence of solutions and multiplicity properties for generalized Yamabe equations on Riemannian manifolds.  Problems of this type arise in conformal Riemannian geometry, astrophysics, and in the theories of thermionic emission, isothermal stationary gas sphere, and gas combustion. The abstract results of this paper are illustrated with Emden-Fowler equations involving sublinear terms at innity. Two examples reveal the analytic setting of this paper. Key words: Three solutions, generalized Yamabe equations, Riemannian manifold, Emden-Fowler problem, variational methods

Existence Results for Dynamic Sturm-Liouville Boundary Value Problems Via Variational Methods

Several conditions ensuring existence of solutions of a dynamic Sturm-Liouville boundary value problem are derived. Variational methods are utilized in the proofs. An example illustrating the main results is given