EUDML

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A note on the existence of two nontrivial solutions of a resonance problem.

To Fu Ma — 1994

Portugaliae Mathematica

Three solutions of a quasilinear elliptic problem near resonance

To Fu Ma; Luis Sanchez — 1997

Mathematica Slovaca

A nonlinear differential equation involving reflection of the argument

To Fu Ma; E. S. Miranda; M. B. de Souza Cortes — 2004

Archivum Mathematicum

We study the nonlinear boundary value problem involving reflection of the argument $- M (\int_{- 1}^{1} {| u^{'} (s) |}^{2} d s) u^{''} (x) = f (x, u (x), u (- x)) x \in [- 1, 1],$ where $M$ and $f$ are continuous functions with $M > 0$ . Using Galerkin approximations combined with the Brouwer’s fixed point theorem we obtain existence and uniqueness results. A numerical algorithm is also presented.