On extension of solutions of Kirchhoff equations

Periodic solutions of forced Kirchhoff equations

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.

Variational Methods and Periodic Solutions of Kirchhoff-type Equations. Ii

In a previous paper [1], the author and Shmel’tser started the construction of an extended Lyusternik–Shnirelman–Morse theory for the study of single-valued and multivalued functionals on the space Ω̂(M) of losed directed curves in a manifold M. The authors applied these methods to the classical problem (Kirchhoffs problem) about the free motion of a rigid body in an ideal incompressible liquid,...

effect of oral presentation on development of l2 learners grammar

this experimental study has been conducted to test the effect of oral presentation on the development of l2 learners grammar. but this oral presentation is not merely a deductive instruction of grammatical points, in this presentation two hypotheses of krashen (input and low filter hypotheses), stevicks viewpoints on grammar explanation and correction and widdowsons opinion on limited use of l1...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Spectral gap global solutions for degenerate Kirchhoff equations

We consider the second order Cauchy problem u +m(|Au|)Au = 0, u(0) = u0, u(0) = u1, where m : [0,+∞) → [0,+∞) is a continuous function, and A is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It is well known that this problem admits local-in-time solutions provided that u0 and u1 are regular enough, depending on the continuity modulus of m, and on the strict/weak hyp...