Nodal solutions for double phase Kirchhoff problems with vanishing potentials

Isernia, Teresa (author), Repovš, Dušan (author)

We consider the following ▫$(p,q)$▫-Laplacian Kirchhoff type problem ▫$$-\left(a+b \int_{\mathbb{R}^3}|\nabla u|^p dx\right)\Delta_pu - \left(c+d \int_{\mathbb{R}^3}|\nabla u|^q dx\right) \Delta_qu$$▫ ▫$$+V(x)(|u|^{p-2}u+|u|^{q-2}u)= =K(x)f(u) \quad \text{in}\mathbb{R}^3,$$▫ where $a,b,c,d>0$ are constants, ▫$\frac{3}{2}<p<q<3$▫, ▫$V:\mathbb{R}^3 \to \mathbb{R}$▫ and ▫$K:\mathbb{R}^3 \to \mathbb{R}$▫ are positive continuous functions allowed for vanishing behavior at infinity, and ▫$f$▫ is a continuous function with quasicritical growth. Using a minimization argument and a quantitative deformation lemma we establish the existence of nodal solutions.

• Language: English
• Keywords: (p, q)-Kirchhoff, nodal solutions, vanishing potentials, Nehari manifold
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication version: Author Accepted Manuscript
• Year: 2021
• Number of pages: Str. 371-396
• Numbering: Vol. 124, Iss. 3-4
• PID: 20.500.12556/RUL-128912
• UDC: 517.956
• ISSN on article: 0921-7134
• DOI: 10.3233/ASY-201648
• COBISS.SI-ID: 33039619
• Publication date in RUL: 16.08.2021

Record is a part of a journal

• Title: Asymptotic analysis
• Shortened title: Asymptot. anal.
• Publisher: IOS Press
• ISSN: 0921-7134
• COBISS.SI-ID: 25030144