Multiplicity of solutions for a nonhomogeneous quasilinear elliptic problem with critical growth

Carvalho, Marcos L. M.; Gonçalves, J. V.; Goulart, Claudiney; Miyagaki, Olı́mpio H.

doi:10.3934/cpaa.2019006

Cited by 2 publications

(2 citation statements)

References 36 publications

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“…Let us consider the case t min{ i} , t max{mi} ≥ 1. The proof for the other cases are analogous which can be found in [9]. Hence we can proceed as in [9,37,38] proving the following inequalities…”

mentioning

confidence: 63%

Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

Carvalho¹,

Silva²,

Goulart³

et al. 2020

Communications on Pure &Amp; Applied Analysis

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It is established existence of bound and ground state solutions for quasilinear elliptic systems driven by (Φ 1 , Φ 2)-Laplacian operator. The main feature here is to consider quasilinear elliptic systems involving both nonsingular nonlinearities combined with indefinite potentials and singular cases perturbed by superlinear and subcritical couple terms. These prevent us to use arguments based on Ambrosetti-Rabinowitz condition and variational methods for differentiable functionals. By exploring the Nehari method and doing a fine analysis on the fibering map associated, we get estimates that allow us unify the arguments to show multiplicity of semi-trivial solutions in both cases.

show abstract

mentioning

confidence: 63%

Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

Carvalho¹,

Silva²,

Goulart³

et al. 2020

Communications on Pure &Amp; Applied Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let us consider the case t min{ℓi} , t max{mi} ≥ 1. The proof for the other cases are analogous which can be found in [10]. Remembering that t min{ℓi} , t max{mi} ≥ 1 and using the fact that t min{ℓi} ≥ 1 we can proceed as in [10,37,38] proving the following inequalities…”

Section: Analysis Of the Fibering Mapsmentioning

confidence: 75%

Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

Carvalho,

Da Silva,

Santos

et al. 2018

Preprint

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It is established existence of bound and ground state solutions for quasilinear elliptic systems driven by (Φ 1 , Φ 2 )-Laplacian operator. The main feature here is to consider quasilinear elliptic systems involving both nonsingular nonlinearities combined with indefinite potentials and singular cases perturbed by superlinear and subcritical couple terms. These prevent us to use arguments based on Ambrosetti-Rabinowitz condition and variational methods for differentiable functionals. By exploring the Nehari method and doing a fine analysis on the fibering map associated, we get estimates that allow us unify the arguments to show multiplicity of semi-trivial solutions in both cases.

show abstract

Multiplicity of solutions for a nonhomogeneous quasilinear elliptic problem with critical growth

Cited by 2 publications

References 36 publications

Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

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