Nonlinear elliptic equations and operators of type L∗Ф ∘ L

Weyer, Jürgen

doi:10.1016/0362-546x(82)90052-9

Cited by 4 publications

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“…The potential results are a consequence of a theorem of Vainberg [12, p. 56]. In order to conclude the maximal cyclical monotonicity of L$>L, it is sufficient that <& has this property [13,14]. The maximality of $ is a consequence of the fact that $ is hemi-continuous and D(O) = H.…”

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confidence: 99%

“…Nonlinear wave equations and eigenvalue problems containing nonlinear operators /((AM, M))AU have been considered by Bazley et al [1,2,3]. In the papers [13,14], the author gave preference to the decomposition of form LQ>L, because this aspect of the operators considered allows the proof of maximal (cyclical) monotonicity, if $ is maximal (cyclically) monotone.…”

Section: Introductionmentioning

confidence: 99%

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Regular solutions of wave equations containing nonlinearities of the type L Φ L

Weyer

1983

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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SynopsisRegular solutions of the forced nonlinear wave equation uu + L4u + LΦLu = r are studied in Hilbert spaces. L is a linear, positive, selfadjoint operator and the nonlinear nucleus Φ(u) = f(|u|2)u is generated by a C1-function f, such that LΦ(Lu) = f(|Lu|2)L2u. If the initial value data u(0) = ϕ and u1(0) = ψ belong to the domain D(Lk+4) and D(Lk+2), respectively, and if rεD(Lk), then there is a (global) solution u(t) such that u ε D(Lk+4), ut ε D(Lk+2) and uuε D(Lk) for all times t. The abstract result is applied to examples in nonlinear elasticity theory.

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confidence: 99%