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On a ▫$p(\cdot)$▫-biharmonic problem with no-flux boundary condition
ID
Boureanu, Maria-Magdalena
(
Author
),
ID
Rǎdulescu, Vicenţiu
(
Author
),
ID
Repovš, Dušan
(
Author
)
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Abstract
The study of fourth order partial differential equations has flourished in the last years, however, a ▫$p(\cdot)$▫-biharmonic problem with no-flux boundary condition has never been considered before, not even for constant ▫$p$▫. This is an important step further, since surfaces that are impermeable to some contaminants are appearing quite often in nature, hence the significance of such boundary condition. By relying on several variational arguments, we obtain the existence and the multiplicity of weak solutions to our problem. We point out that, although we use a mountain pass type theorem in order to establish the multiplicity result, we do not impose an Ambrosetti-Rabinowitz type condition, nor a symmetry condition, on our nonlinearity ▫$f$▫.
Language:
English
Keywords:
variable exponent
,
new variable exponent subspace
,
▫$p(\cdot)$▫-biharmonic operator
,
nonlinear elliptic problem
,
weak solutions
,
existence
,
multiplicity
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Year:
2016
Number of pages:
Str. 2505-2515
Numbering:
Vol. 72, iss. 9
PID:
20.500.12556/RUL-111106
UDC:
517.956
ISSN on article:
0898-1221
DOI:
http://dx.doi.org/10.1016/j.camwa.2016.09.017
COBISS.SI-ID:
17789785
Publication date in RUL:
24.09.2019
Views:
887
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426
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Record is a part of a journal
Title:
Computers & mathematics with applications
Shortened title:
Comput. math. appl.
Publisher:
Elsevier
ISSN:
0898-1221
COBISS.SI-ID:
15336965
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