Nodal solutions for double phase Kirchhoff problems with vanishing potentials

Article type: Research Article

Authors: Isernia, Teresa^{a; *} | Repovš, Dušan D.^b

Affiliations: [a] Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 12, 60131 Ancona, Italy | [b] Faculty of Education, and Faculty of Mathematics and Physics, University of Ljubljana & Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia. E-mail: dusan.repovs@guest.arnes.si

Correspondence: [*] Corresponding author. E-mail: t.isernia@univpm.it.

Abstract: We consider the following (p,q)-Laplacian Kirchhoff type problem −(a+b∫R3|∇u|pdx)Δpu−(c+d∫R3|∇u|qdx)Δqu+V(x)(|u|p−2u+|u|q−2u)=K(x)f(u)in R3, where a,b,c,d>0 are constants, 32<p<q<3, V:R3→R and K:R3→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.

Keywords: (p, q)-Kirchhoff, nodal solutions, vanishing potentials, Nehari manifold

DOI: 10.3233/ASY-201648

Journal: Asymptotic Analysis, vol. 124, no. 3-4, pp. 371-396, 2021