The dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation. (English) Zbl 0960.34013

Grossinho, M. R.; Tersian, St. A.

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 41, No. 3-4, 417-431 (2000).

The author investigates sufficient conditions for the existence of solutions to equations of the form \[ u'''' + g(u(x)) = 0,u''(0)=-f(-u'(0)),u'''(0)=-h(u(0)),u''(1)=0,u'''(1)=0. \]
The main assumption is that \(g\) is discontinuous at a point. And the method is Clarke’s dual action principle following the idea of A. Ambrosetti and M. Badiale [J. Math. Anal. Appl. 140, No. 2, 363-373 (1989; Zbl 0687.35033)].

Reviewer: Yujun Dong (Nanjing)

MSC:

34B15

Nonlinear boundary value problems for ordinary differential equations

Keywords:

nonlinear boundary value problems; variational methods; dual action principle; discontinuous nonlinearities

Citations:

Zbl 0687.35033