A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the help of Kirchhoff- Love plate theory. The thermoelastic damping of micro-beam resonators is analyzed by using the normal mode a...

We consider Kirchhoff equations for vibrating strings and elastic membranes under the action of an external forcing of period 2π/ω and small amplitude ε. We prove existence, regularity and local uniqueness of 2π/ω-periodic solutions of order ε by means of a Nash-Moser iteration scheme; the results hold for parameters (ω, ε) in a Cantor-like set which has asymptotically full measure for ε→ 0.

In recent years, various Kirchhoff type problems have been extensively investigated by many authors due to their theoretical and practical importance, such problems are often referred to as being nonlocal because of the presence of the integral over the entire domain Ω. It is well known that this problem is analogous to the stationary problem of a model introduced by Kirchhoff [1]. More precise...

We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentia...

Abstract This paper presents a simple and systematic method to show how the potentials in the Lorentz, Coulomb, Kirchhoff, velocity and temporal gauges yield the same retarded electric and magnetic fields. The method appropriately uses the dynamical equations for the scalar and vector potentials to obtain two wave equations, whose retarded solutions lead to the electric and magnetic fields. The...