Multiparameter direct variational solutions for linear dissipative oscillators

Hartley Series Direct Method for Variational Problems

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

Nontrivial Solutions for Asymptotically Linear Variational Inequalities

The aim of this paper is to extend to variational inequalities a result of Amann and Zehnder’s, refined by Chang (see [1, 6, 14]), concerning the existence of nontrivial solutions for a semilinear elliptic boundary value problem, when the nonlinearity is asymptotically linear, is zero at zero and its derivative has a suitable jump between zero and infinity. In the constrained problem studied he...

Representation of Dissipative Solutions to a Nonlinear Variational Wave Equation

The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with the conservative case, here the source terms are discontinuous and the discontinuities are not always crossed transversally. Solutions to the semilinear system...

Positive Solutions for Multiparameter Semipositone Discrete Boundary Value Problems via Variational Method

Approximate analytic solutions for non-linear oscillators with fractional-order restoring force by means of the optimal variational iteration method

In this paper, a new approach, namely the optimal variational iteration method (OVIM) was proposed to investigate oscillators with fractional-power nonlinearities. It was illustrated that this approach is very effective and convenient and does not require linearization or small parameter. Unlike other classical iteration methods, only one iteration leads to highly accurate results, due to a rig...