On a ▫$p(\cdot)$▫-biharmonic problem with no-flux boundary condition

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

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 (dk_c)
• Tipology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Year: 2016
• Number of pages: str. 2505-2515
• Numbering: Vol. 72, iss. 9
• UDC: 517.956
• ISSN on article: 0898-1221
• DOI: http://dx.doi.org/10.1016/j.camwa.2016.09.017
• COBISS.SI-ID: 17789785
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• Title: Computers & mathematics with applications
• Shortened title: Comput. math. appl.
• Publisher: Pergamon Press
• ISSN: 0898-1221
• COBISS.SI-ID: 15336965