We obtain results on nonexistence of nontrivial nonnegative solutions for some elliptic inequalities with functional parameters involving the p(x)–Laplacian operator. The proof is based on the test function method.
REFERENCES
1.
L.
Diening
, P.
Harjulehto
, P.
Hästö
and M.
Růžička
, Lebesgue and Sobolev Spaces with Variable Exponents
(Springer Verlag
, Berlin
, 2011
).2.
X.
Fan
, Math. Nachr.
284
, 1435
âĂŞ-1445
(2011
).3.
4.
Yu.
Alkhutov
and V.
Zhikov
, Sbornik: Mathematics
205
, 307
–318
(2014
).5.
6.
J. P.
Pinasco
, Nonl. Anal.: TMA
71
, 1094
–âĂŞ1099
(2009
).7.
8.
E.
Galakhov
and O.
Salieva
, Journ. Math. Anal. and Appl.
408
, 102
–113
(2013
).9.
E.
Galakhov
and O.
Salieva
, “Blow-up for nonlinear inequalities with singularities on unbounded sets
,” in Current Trends in Analysis and Its Applications
, Proceedings of the IXth ISAAC Congress
, edited by V.
Mityushev
and M.
Ruzhansky
(Birkhäuser, Basel
, 2015
), pp. 299
–305
.10.
E.
Galakhov
, O.
Salieva
and L.
Uvarova
, Electronic Journal of Differential Equations
, No. 216
, 1
–12
(2014
).11.
L.
Diening
, “Theoretical and numerical results for electrorheological fluids
,” Ph.D. thesis, University of Freiburg im Breslau
, Germany
(2002
).12.
T. C.
Halsey
, Sciences
258
(5083
), 761
âĂŞ-766
(1992
).13.
M.
Růžička
, Electrorheological Fluids: Modeling and Mathematical Theory
(Springer-Verlag
, Berlin
, 2002
).
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