On a p(.)-biharmonic problem with no-flux boundary condition

Maria-Magdalena Boureanu (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

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 ▫$f$▫.

Keywords

variable exponent;new variable exponent subspace;▫$p(\cdot)$▫-biharmonic operator;nonlinear elliptic problem;weak solutions;existence;multiplicity;

Data

Language:	English
Year of publishing:	2016
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956
COBISS:	17789785
ISSN:	0898-1221
Views:	481
Downloads:	305
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 2505-2515
Volume:	ǂVol. ǂ72
Issue:	ǂiss. ǂ9
Chronology:	2016
DOI:	http://dx.doi.org/10.1016/j.camwa.2016.09.017
ID:	11232027