Electron. J. Diff. Eqns., Vol. 2005(2005), No. 144, pp. 1-8.

Nonlinear boundary conditions for elliptic equations

Pablo Amster, Maria Cristina Mariani, Osvaldo Mendez

This work is devoted to the study of the elliptic equation $\Delta u = f(x,u)$ in a bounded domain $\Omega\subset \mathbb{R}^n$ with a nonlinear boundary condition. We obtain various existence results applying coincidence degree theory and the method of upper and lower solutions.

Submitted November 15, 2004. Published December 8, 2005.
Math Subject Classifications: 35J25, 35J60.
Key Words: Nonlinear elliptic problems; nonlinear boundary conditions; topological methods.

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Pablo Amster
Departamento de Matemática
FCEyN -Universidad de Buenos Aires
Ciudad Universitaria, Pabellóon I
(1428) Buenos Aires, Argentina
email: pamster@dm.uba.ar
María Cristina Mariani
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003-0001, USA
email: mmariani@nmsu.edu
Osvaldo Méndez
Department of Mathematics
500W University Ave., 124 Bell Hall
The University of Texas at El Paso
El Paso, TX 79968, USA
email: mendez@math.utep.edu

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