Affiliation:
1. Department of Mathematics Birla Institute of Technology and Science Pilani, Pilani Campus Rajasthan India
Abstract
This paper aims to establish the existence of a weak solution for the nonlocal problem:
where
is a bounded and smooth domain containing two open and connected subsets
and
such that
and
is the
‐Laplace operator. We assume that
reduces to
in
and to
in
, the nonlinear function
acts as
on
and as
on
for sufficiently large
. To establish the existence results in a Musielak–Sobolev space, we use a variational technique based on the mountain pass theorem.
Subject
General Engineering,General Mathematics
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