Ground state and nodal solutions for a class of double phase problems

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

We consider a double phase problem driven by the sum of the ▫$p$▫-Laplace operator and a weighted ▫$q$▫-Laplacian ▫$(q<p)$▫, with a weight function which is not bounded away from zero. The reaction term is ▫$(p-1)$▫-superlinear. Employing the Nehari method, we show that the equation has a ground state solution of constant sign and a nodal (sign-changing) solution.

• Language: English
• Keywords: double phase operator, weight function, superlinear reaction, Nehari manifold, ground state solution, nodal solution
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 1-15
• Numbering: Vol. 71, Iss. 1, art. 15
• PID: 20.500.12556/RUL-116614
• UDC: 517.956.2
• ISSN on article: 0044-2275
• DOI: 10.1007/s00033-019-1239-3
• COBISS.SI-ID: 18868057
• Publication date in RUL: 29.05.2020

Record is a part of a journal

• Title: Zeitschrift für angewandte Mathematik und Physik
• Shortened title: Z. angew. Math. Phys.
• Publisher: Birkhaeuser Verlag
• ISSN: 0044-2275
• COBISS.SI-ID: 26662656