In the present work we study the multiplicity and concentration of positive solutions for the following class of Kirchhoff problems: -{ϵ2 a + ϵb R3 δu 2 dx ) Δu + V (x)u= f(u) + γu5 in R3 , u ϵ H1 (R3) , u > 0 in R3 , where ϵ > 0 is a small parameter, a , b > 0 are constants, γ ϵ { 0 , 1 }, V is a continuous positive potential with a local minimum, and f is a superlinear continuous function with subcritical growth. The main results are obtained through suitable variational and topological arguments. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. Our theorems extend and improve in several directions the studies made in (Adv. Nonlinear Stud. 14 (2014), 483-510; J. Differ. Equ. 252 (2012), 1813-1834; J. Differ. Equ. 253 (2012), 2314-2351).
On a class of Kirchhoff problems via local mountain pass / Ambrosio, V.; Repovs, D.. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 126:1-2(2022), pp. 1-43. [10.3233/ASY-201660]
On a class of Kirchhoff problems via local mountain pass
Ambrosio V.;
2022-01-01
Abstract
In the present work we study the multiplicity and concentration of positive solutions for the following class of Kirchhoff problems: -{ϵ2 a + ϵb R3 δu 2 dx ) Δu + V (x)u= f(u) + γu5 in R3 , u ϵ H1 (R3) , u > 0 in R3 , where ϵ > 0 is a small parameter, a , b > 0 are constants, γ ϵ { 0 , 1 }, V is a continuous positive potential with a local minimum, and f is a superlinear continuous function with subcritical growth. The main results are obtained through suitable variational and topological arguments. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. Our theorems extend and improve in several directions the studies made in (Adv. Nonlinear Stud. 14 (2014), 483-510; J. Differ. Equ. 252 (2012), 1813-1834; J. Differ. Equ. 253 (2012), 2314-2351).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
