Asadollah Aghajani, Alireza Mosleh Tehrani
Abstract:
We derive a priori bounds for positive supersolutions of
,
where p>1 and
is the p-Laplace operator, in a smooth bounded
domain of
with zero Dirichlet boundary conditions.
We apply our results to the nonlinear elliptic eigenvalue problem
,
with Dirichlet boundary condition,
where
is a nondecreasing continuous differentiable function on
such that f(0)>0,
is superlinear at infinity,
and give sharp upper and lower bounds for the extremal parameter
.
In particular, we consider the nonlinearities
and
()
and give explicit estimates on
.
As a by-product of
our results, we obtain a lower bound for the principal eigenvalue of the
p-Laplacian that improves obtained results in the recent literature
for some range of p and N.
Submitted June 10, 2015. Published February 14, 2017.
Math Subject Classifications: 35J66, 35J92, 35P15.
Key Words: Nonlinear eigenvalue problem; estimates of principal eigenvalue;
extremal parameter.
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Asadollah Aghajani School of Mathematics Iran University of Science and Technology Narmak, Tehran 16844-13114, Iran. phone +9821-73913426. Fax +9821-77240472 email: aghajani@iust.ac.ir | |
Alireza Mosleh Tehrani School of Mathematics Iran University of Science and Technology Narmak, Tehran 16844-13114, Iran email: amtehrani@iust.ac.ir |
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