Electron. J. Diff. Eqns., Vol. 2001(2001), No. 63, pp. 1-10.

On the multiplicity of solutions for a fully nonlinear Emden-Fowler equation

Marco Squassina

We are concerned with the existence of two solutions for a fully nonlinear Emden-Fowler type equation. One solution is obtained via local minimization while the second solution follows by a mountain pass argument. A non-existence result in strictly star-shaped domains is also proven.

Submitted April 4, 2001. Published October 3, 2001.
Math Subject Classifications: 35D05, 58E05.
Key Words: Trudinger-Moser inequality, Euler's equations, exponential growth, Palais-Smale condition

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Marco Squassina
Universita Cattolica del S.C.
Dipartimento di Matematica & Fisica
Via Musei 41, 25121
Brescia, Italy
e-mail: squassin@dmf.unicatt.it

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