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dc.contributor.authorDinca, George ( )
dc.contributor.authorMatei, Pavel ( Orcid Icon 0000-0001-8883-3442 )
dc.identifier.citationDinca, G., & Matei, P. (2007). Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces. Electronic Journal of Differential Equations, 2007(93), pp. 1-47.en_US

Let α : ℝ → ℝ be a strictly increasing odd continuous function with limt→+∞ α(t) = +∞ and A(t) = ∫t0 α(s) ds, t ∈ ℝ, the N-function generated by α. Let Ω be a bounded open subset of ℝN, N ≥ 2, T[u, u] a nonnegative quadratic form involving the only generalized derivatives of order m of the function u ∈ Wm0 EA(Ω) and gα : Ω x ℝ → ℝ, |α| < m, be Carathéodory functions.

We study the problem

Jαu = ∑|α| (-1)|α| Dα gα(x, Dαu) in Ω,
Dαu = 0 on ∂Ω, |α| ≤ m - 1,

where Jα is the duality mapping on (Wm0 EA(Ω), ∥ ⋅ ∥m,A), subordinated to the gauge function α (given by (1.5)) and

∥u∥m,A = ∥√T[u, u]∥(A),

∥ ⋅ ∥A being the Luxemburg norm on EA(Ω).

By using the Leray-Schauder topological degree and the mountain pass theorem of Ambrosetti and Rabinowitz, the existence of nontrivial solutions is established. The results of this paper generalize the existence results for Dirichlet problems with p-Laplacian given in [12] and [13].

dc.format.extent47 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectA priori estimateen_US
dc.subjectCritical pointsen_US
dc.subjectOrlicz-Sobolev spacesen_US
dc.subjectLeray-Schauder topological degreeen_US
dc.subjectDuality mappingen_US
dc.subjectNemytskij operatoren_US
dc.subjectMountain Pass Theoremen_US
dc.titleVariational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spacesen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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