Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

By Gabriele Bonanno, Giovanni Molica Bisci. 2009

248 citations recorded by the source corpus.

The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c6f71112cdc2c0414ab5bb3b9b38bb281292c69a

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Arbitrarily small weak solutions for a nonlinear eigenvalue problem in Orlicz–Sobolev spaces (2012, methodology): “The main tool in order to prove our multiplicity result is the following critical points theorem obtained in [4] that we recall here in a convenient form.”
Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces (2012, methodology): “The main tool in order to prove our multiplicity result is the following critical point theorem obtained in [27] that we recall here in a convenient form; see also the variational principle of Ricceri [28].”
Infinitely many solutions for a fourth-order elastic beam equation (2011, background): “1 of [2], which is a more precise version of Ricceri’s Variational Principle [9, Theorem 2.”
Infinitely many solutions for a class of discrete non-linear boundary value problems (2009, unknown): “1) obtained in [13] (see also [14,15]).”