Nonlinear elliptic differential equations with multivalued nonlinearities

Fiacca, Antonella; Matzakos, Nikolaos; Papageorgiou, Nikolaos S.; Servadei, Raffaella

doi:10.1007/bf02829620

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On the Convergence Of The Palais-smale Sequence1

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2013

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“…Lemma 5.1 Let (u n ) ⊂ W 1,Φ 0 (Ω) be the sequence in (12). Extend each u n to R N by setting u n = 0 on R N \Ω.…”

Section: On the Convergence Of The Palais-smale Sequencementioning

confidence: 99%

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On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth

Gonçalves¹,

Carvalho²

2013

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We develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity and compactness techniques to investigate existence of solution of the multivalued equation −∆ Φ u ∈ ∂j(., u) + λh in Ω, where Ω ⊂ R N is a bounded smooth domain, Φ : R −→ [0, ∞) is a suitable N-function, ∆ Φ is the corresponding Φ-Laplacian, λ > 0 is a parameter, h : Ω → R is integrable and ∂j(., u) is the subdifferential of a function j associated with critical growth.Dedicated to Bernhard Ruf on the occasion of his 60 th birthday.

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“…Lemma 5.1 Let (u n ) ⊂ W 1,Φ 0 (Ω) be the sequence in (12). Extend each u n to R N by setting u n = 0 on R N \Ω.…”

Section: On the Convergence Of The Palais-smale Sequencementioning

confidence: 99%

“…There is a broad literature on multivalued variational equations, see e.g. Halidias & Naniewicz [17], Fiacca, Matzakos & Papageorgiou [12], Alves, Goncalves & Santos [4], Filippakis & Papageorgiou [13], Kyritsi & Papageorgiou [19], Naniewicz [24] and references therein.…”

Section: Introdutionmentioning

confidence: 99%

On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth

Gonçalves¹,

Carvalho²

2013

Preprint

View full text Add to dashboard Cite

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Nonlinear elliptic differential equations with multivalued nonlinearities

Cited by 1 publication

References 19 publications

On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth

On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth

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