Nonlinear Differential Equations,

Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 301-308.

### An elliptic problem with arbitrarily small positive solutions

Pierpaolo Omari & Fabio Zanolin

**Abstract:**

We show that for each
,
the problem

in
,

on

has a sequence of positive solutions
with
decreasing to zero. We assume that
and that
,
where
.
We stress that no condition on the sign of
is imposed.
Published October 13, 2000.

Math Subject Classifications: 35J65, 34B15, 34C25, 47H15.

Key Words: Quasilinear elliptic equation, positive solution,
upper and lower solutions, time-mapping estimates.

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Pierpaolo Omari

Dipartimento di Scienze Matematiche

Universita, Piazzale Europa 1

I-34127 Trieste, Italy

e-mail: omari@univ.trieste.it
Fabio Zanolin

Dipartimento di Matematica e Informatica

Universita, Via delle Scienze 206

I--33100 Udine, Italy

e-mail: zanolin@dimi.uniud.it

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