Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary value problems associated with singular strongly nonlinear
  equations with functional terms   We study boundary value problems associated with singular, strongly nonlinear
differential equations with functional terms of type
$$\big(\Phi(k(t)\,x'(t))\big)' + f(t,\mathcal{G}_x(t))\,\rho(t, x'(t)) = 0$$ on
a compact interval $[a,b]$. These equations are quite general due to the
presence of a strictly increasing homeomorphism $\Phi$, the so-called
$\Phi$-Laplacian operator, of a nonnegative function $k$, which may vanish on a
set of null measure, and moreover of a functional term $\mathcal{G}_x$. We look
for solutions, in a suitable weak sense, which belong to the Sobolev space
$W^{1,1}([a,b])$. Under the assumptions of the existence of a well-ordered pair
of upper and lower solutions and of a suitable Nagumo-type growth condition, we
prove an existence result by means of fixed point arguments.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess