Search

In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced nonlinear second order differential equations with delayed argument in the form x″(t)+q(t)x(τ(t))γsgnx(τ(t))=f(t) in the linear (γ=1) and the superlinear (γ>1) cases. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of periodic solutions of the second order differential equations . Using continuation lemma, we obtain the existence of periodic solutions provided that () is sublinear when x tends to positive infinity and satisfies a new condition where M, d are two positive constants. [Copyright &y& Elsevier]

Abstract: We let Ω be a smooth bounded domain of and a sequence of functions such that in . We consider a sequence of functions such that in Ω for all . We address in this paper the question of the asymptotic behavior of the ''s when . The corresponding problem in dimension 2 was considered by Brézis and Merle, and Li and Shafrir (among others), where a blow-up phenomenon was described and where a quantization of this blow-up was proved. Surprisingly, as shown by Adimurthi, Struwe and the author in [Adimurthi, F. Robert and M. Struwe, Concentration phenomena for Liouville equations in dimension four, J. Eur. Math. Soc., in press, available on http://www-math.unice.fr/~frobert], a similar quantization phenomenon does not hold for this fourth-order problem. Assuming that the ''s are radially symmetrical, we push further the analysis of the mentioned work. We prove that there are exactly three types of blow-up and we describe each type in a very detailed way. [Copyright &y& Elsevier]

Abstract: The problem of a classification of robust homoclinic cycles in low-dimensional spaces has been frequently asked in recent years. In this paper, we resume the results in and and we solve the problem in in the case of orientation-preserving group actions. [Copyright &y& Elsevier]

New existence and uniqueness proofs are given for the solutions of the equations governing the self-similar compressible boundary layer (Falkner–Skan equations). The properties of the solutions are studied and some bounds on important quantities are concluded. The paper is restricted to favourable pressure gradients and to wall cooling. [Copyright &y& Elsevier]