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 problemwhere Moreover, the function ur is a weak solution to the corresponding Euler–Lagrange equationfor 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.
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Let m : [0, [ Ä [0, [ be an increasing continuous function with m(t)=0 if and only if t=0, m(t) Ä as t Ä and 0/R N a bounded domain. In this paper we show that for every r>0 the problemhas an infinite number of eigenfunctions on the level set 0 M(|{u|)=r, where M(t)= |t| 0 m(s) ds and g : R Ä R is odd satisfying some growth condition. Moreover, we show that the sequence of associated eigenvalues tends to infinity. We emphasize that no q 2 -condition is needed for M or for its conjugate, so the associated functionals are not continuously differentiable, in general.
2000Academic Press
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