caa a22 4500 388108606 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500027505 doi S0308210500027505 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500027505 An eigenvalue problem for generalized Laplacian in Orlicz—Sobolev spaces [Elektronische Daten] Let m: [ 0, ∞) → [ 0, ∞) be an increasing continuous function with m(t) = 0 if and only if t = 0, m(t) → ∞ as t → ∞ and Ω C ℝN a bounded domain. In this note we show that for every r > 0 there exists a function ur solving the minimization problem where Moreover, the function ur is a weak solution to the corresponding Euler-Lagrange equation for some λ > 0. We emphasize that no Δ2-condition is needed for M or M; so the associated functionals are not continuously differentiable, in general. Copyright © Royal Society of Edinburgh 1999 Mustonen Vesa Department of Mathematical Sciences, University of Oulu, FIN 90570, Oulu, Finland (vesa.mustonen@oulu.fi Tienari Matti Department of Mathematical Sciences, University of Oulu, FIN 90570, Oulu, Finland matti.tienari@oulu.fi Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 153-163 0308-2105 129:1<153 1999 129 PRM https://doi.org/10.1017/S0308210500027505 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500027505 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mustonen Vesa Department of Mathematical Sciences, University of Oulu, FIN 90570, Oulu, Finland (vesa.mustonen@oulu.fi NATIONALLICENCE 700 1- Tienari Matti Department of Mathematical Sciences, University of Oulu, FIN 90570, Oulu, Finland matti.tienari@oulu.fi NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 153-163 0308-2105 129:1<153 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge