Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models

Abstract For studying the evolution of transverse deflection an extensible beam derived from connection mechanics, we investigate initial boundary value problem nonlinear equation with linear strong damping term, weak and source term. The key idea our analysis is to describe invariant manifold via Nehari manifold. To establish results global well-posedness solution, consider at three different energy levels, i.e., subcritical level, critical arbitrarily high level. We first obtain local existence solution by using contraction mapping principle. Then, in framework potential well, existence, nonexistence, asymptotic behavior for both level In end, nonexistence