Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactnessLi, Lin (Avtor)
Rǎdulescu, Vicenţiu (Avtor)
Repovš, Dušan (Avtor)
mountain passEkeland variational principlenonlocal Kirchhoff equationWe study the following Kirchhoff equation ▫$$ - \left( 1 + b \int_{\mathbb{R}^3} |\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u), \quad x \in \mathbb{R}^3. $$▫ A feature of this paper is that the nonlinearity ▫$f$▫ and the potential ▫$V$▫ are indefinite, hence sign-changing. Under some appropriate assumptions on ▫$V$▫ and ▫$f$▫, we prove the existence of two different solutions of the equation via the Ekeland variational principle and the mountain pass theorem.20162019-09-24 07:56:53Članek v reviji111102sl