Global solvability for the degenerate Kirchhoff equation with real analytic data

Multiple solutions for a class of Kirchhoff type problems with concave nonlinearity

“…(1.2) received much attention only after Lions [13] proposed an abstract framework to the problem. Later, P. D'Ancona and S. Spagnolo [10] studied the global solvability for the degenerate Kirchhoff equation with real analytic data. Recently, many authors studied the following elliptic Kirchhoff type problems…”

Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation

“…In the sequel, we would like to mention some important works on this subject. Regarding the wellposedness of problem (1.1), the analytic case is rather known in general dimensions, as, for instance, [8], [9] and [25]. In what concerns solutions for (1.1) lying in Sobolev spaces and, as far as we know, the results presented in the literature are only local in time, as, for example, [1] and [24].…”

Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problems

“…which is has attracted much attention after Lions's paper [31], where a functional analysis frame work for the problem was proposed; see, e.g., [6,12,16] for some interesting results. Moreover, nonlocal problems like…”