Meta-heuristics have already received considerable attention in various engineering optimization fields. As one of the most rewarding tasks, eigenvalue optimization of truss structures is concerned in this study. In the proposed problem formulation the fundamental eigenvalue is to be maximized for a constant structural weight. The optimum is searched using Particle Swarm Optimization, PSO and i...

In the case of not requiring the nonlinear term to be monotone or convex, we study the existence of positive solutions for second-order periodic boundary value problem by using the first eigenvalue of the corresponding linear problem and fixed point index theory. The work significantly improves and generalizes the main results of J. Graef et al. [A periodic boundary value problem with vanishing...

We study geometrical conditions guaranteeing the validity of the classical GaffneyFriedrichs estimate ‖u‖H1,2(Ω) ≤ C ( ‖du‖L2(Ω) + ‖δu‖L2(Ω) + ‖u‖L2(Ω) ) (0.1) granted that the differential form u has a vanishing tangential or normal component on ∂Ω. Our main result is that (0.1) holds provided Ω satisfies a suitable convexity assumption. In the Euclidean setting, a uniform exterior ball condit...

We establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resonance at infinity and at the origin can occur with different weights. Our main tool is the computation ...

It is shown that for every 1 ≤ s ≤ n, the probability that the s-th largest eigenvalue of a random symmetric n-by-n matrix with independent random entries of absolute value at most 1 deviates from its median by more than t is at most 4e−t 2/32s2 . The main ingredient in the proof is Talagrand’s Inequality for concentration of measure in product spaces.

We consider a second order operator with analytic coefficients whose principal symbol vanishes exactly to order two on a symplectic real analytic manifold. We assume that the first (non degenerate) eigenvalue vanishes on a symplectic submanifold of the characteristic manifold. In the C∞ framework this situation would mean a loss of 3/2 derivatives (see [5]). We prove that this operator is analy...

Finding approximations to the eigenvalues of nonlinear eigenvalue problems is a common problem which arises from many complex applications. In this paper, iterative algorithms for finding approximations to the eigenvalues of nonlinear eigenvalue problems are verified. These algorithms use an efficient numerical approach for calculating the first and second derivatives of the determinant of the ...

This paper presents a combined adaptive finite element method with an iterative algebraic eigenvalue solver for a symmetric eigenvalue problem of asymptotic quasi-optimal computational complexity. The analysis is based on a direct approach for eigenvalue problems and allows the use of higher-order conforming finite element spaces with fixed polynomial degree. The asymptotic quasi-optimal adapti...

In this paper, a rigorous convergence and error analysis of a Galerkin boundary element method for the Dirichlet Laplacian eigenvalue problem is presented. The formulation of the eigenvalue problem in terms of a boundary integral equation yields a nonlinear boundary integral operator eigenvalue problem. This nonlinear eigenvalue problem and its Galerkin approximation are analyzed in the framewo...