Advances in Differential Equations

On some general semilinear elliptic problems with nonlinear boundary conditions

Bernard Brighi and Mythily Ramaswamy

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We investigate the existence of solutions for a large class of semilinear elliptic problems with nonlinear Neumann boundary conditions. We study separately the one-dimensional case and show how to count the solutions. In higher dimension we give existence results under some compactness assumption.

Article information

Adv. Differential Equations, Volume 4, Number 3 (1999), 369-390.

First available in Project Euclid: 15 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 34B15: Nonlinear boundary value problems 35K60: Nonlinear initial value problems for linear parabolic equations


Brighi, Bernard; Ramaswamy, Mythily. On some general semilinear elliptic problems with nonlinear boundary conditions. Adv. Differential Equations 4 (1999), no. 3, 369--390.

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