We show the existence of infinitely many positive solutions u ∈ H1(R2) to the equation −Delta u + a(x)u = u^p, with p > 1 , without asking, on the positive potential a(x), any symmetry assumption as inWei and Yan (Calc Var Partial Differ Equ 37, 423–439, 2010) or Devillanova and Solimini (Adv Nonlinear Studies 12, 173–186, 2012) or small oscillation assumption as in Cerami et al. (Commun Pure Appl Math, doi:10.1002/cpa.21410, 2012) 6 and in Weiwei and Wei (Infinitely many positive solutions for Nonlinear equations with non-symmetric Potential, 2012).
Infinitely many positive solutions to some nonsymmetric scalar field equations: the planar case / Devillanova, G; Solimini, S. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 52:3-4(2015), pp. 0736.857-0736.898. [10.1007/s00526-014-0736-7]
Infinitely many positive solutions to some nonsymmetric scalar field equations: the planar case
Devillanova G;Solimini S
2015-01-01
Abstract
We show the existence of infinitely many positive solutions u ∈ H1(R2) to the equation −Delta u + a(x)u = u^p, with p > 1 , without asking, on the positive potential a(x), any symmetry assumption as inWei and Yan (Calc Var Partial Differ Equ 37, 423–439, 2010) or Devillanova and Solimini (Adv Nonlinear Studies 12, 173–186, 2012) or small oscillation assumption as in Cerami et al. (Commun Pure Appl Math, doi:10.1002/cpa.21410, 2012) 6 and in Weiwei and Wei (Infinitely many positive solutions for Nonlinear equations with non-symmetric Potential, 2012).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
