Nodal solutions for double phase Kirchhoff problems with vanishing potentialsIsernia, Teresa (Avtor) Repovš, Dušan (Avtor) (pq)-Kirchhoffnodal solutionsvanishing potentialsNehari manifoldWe 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.20212021-08-16 07:29:23Neznano128912UDK: 517.956ISSN pri članku: 0921-7134DOI: 10.3233/ASY-201648COBISS_ID: 33039619sl