Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sign changing solution for a double phase problem with nonlinear
  boundary condition via the Nehari manifold   In this paper we study quasilinear elliptic equations driven by the so-called
double phase operator and with a nonlinear boundary condition. Due to the lack
of regularity, we prove the existence of multiple solutions by applying the
Nehari manifold method along with truncation and comparison techniques and
critical point theory. In addition, we can also determine the sign of the
solutions (one positive, one negative, one nodal). Moreover, as a result of
independent interest, we prove for a general class of such problems the
boundedness of weak solutions.

7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an