Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely many solutions for three classes of self-similar equations,
  with the $p$-Laplace operator   We study the global solution curves, and prove the existence of infinitely
many positive solutions for three classes of self-similar equations, with
$p$-Laplace operator. In case $p=2$, these are well-known problems involving
the Gelfand equation, the equation modeling electrostatic
micro-electromechanical systems (MEMS), and a polynomial nonlinearity. We
extend the classical results of D.D. Joseph and T.S. Lundgren \cite{JL} to the
case $p \ne 2$, and we generalize the main result of Z. Guo and J. Wei
\cite{GW} on the equation modeling MEMS.

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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys