Einführung in die Funktionalanalysis

Meise, Reinhold; Vogt, Dietmar

doi:10.1007/978-3-322-80310-8

Cited by 66 publications

(58 citation statements)

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“…Due to (3.1) it holds Γ k ∈ ∂j(x, U k (x)) a.a. in R N and for all k. Immediately, the boundedness of Γ k in L q is a consequence of condition (j2) and by using the diagonal process of Cantor one shows the existence of a weakly Entire Extremal Solutions for Elliptic Inclusions 69 convergent subsequence of (Γ k ), still denoted by Γ k . In fact, since L q is a reflexive Fréchet space for 1 < q < ∞ (see [12,Theorem 25.15]), we have…”

Section: Resultsmentioning

confidence: 99%

Entire Extremal Solutions for Elliptic Inclusions of Clarke’s Gradient Type

Winkert¹

2010

Z. Anal. Anwend.

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Abstract. We consider multivalued quasilinear elliptic problems of hemivariational type in all of R N given byand show the existence of entire extremal solutions by applying the method of sub-and supersolutions without imposing any condition at infinity. Due to the unboundedness of the domain, standard variational methods cannot be applied. The novelty of our approach is on the one hand to obtain entire solutions and on the other hand that Clarke's generalized gradient need only satisfies a natural growth condition. In the last section conditions are provided that ensure the existence of nontrivial positive solutions.

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Section: Resultsmentioning

confidence: 99%

Entire Extremal Solutions for Elliptic Inclusions of Clarke’s Gradient Type

Winkert¹

2010

Z. Anal. Anwend.

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“…For the theory of one-dimensional manifolds we refer to [47] although the results are very classical and known much earlier. For functional analytic tools see [36]. Now, we present the organization of the paper in which we look at the considered problems from the functional analytic or operator theoretical point of view.…”

Section: Abel's Functional Equation On Spaces 457 Has a Real Analyticmentioning

confidence: 99%

Abel’s Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions

Bonet

Domański

2014

Integr. Equ. Oper. Theory

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Abstract.We obtain full description of eigenvalues and eigenvectors of composition operators Cϕ : A (R) → A (R) for a real analytic self map ϕ : R → R as well as an isomorphic description of corresponding eigenspaces. We completely characterize those ϕ for which Abel's equation f • ϕ = f + 1 has a real analytic solution on the real line. We find cases when the operator Cϕ has roots using a constructed embedding of ϕ into the so-called real analytic iteration semigroups.Mathematics Subject Classification. Primary 47B33, 46E10, 39B12; Secondary 47A15, 47A75, 39B22, 30D05.

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“…For standard results from functional analysis, we refer to the book of Meise and Vogt [23]. where the supremum is taken over all plurisubharmonic functions u : G -» [-00, 0[ with u(w) < log\w\ + O(l) as w -0 (see Klimek [16]).…”

Section: A Criterion For a Differential Operator To Admit A Solution mentioning

confidence: 99%