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Displaying similar documents to “Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues”

Existence and bifurcation results for a class of nonlinear boundary value problems in ( 0 , ∞ )

Wolfgang Rother (1991)

Commentationes Mathematicae Universitatis Carolinae

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We consider the nonlinear Dirichlet problem - u ' ' - r ( x ) | u | σ u = λ u in ( 0 , ∞ ) , u ( 0 ) = 0 and lim x → ∞ u ( x ) = 0 , and develop conditions for the function r such that the considered problem has a positive classical solution. Moreover, we present some results showing that λ = 0 is a bifurcation point in W 1 , 2 ( 0 , ∞ ) and in L p ( 0 , ∞ ) ( 2 ≤ p ≤ ∞ ) .

Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Jan Malý (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let u be a weak solution of a quasilinear elliptic equation of the growth p with a measure right hand term μ . We estimate u ( z ) at an interior point z of the domain Ω , or an irregular boundary point z ∈ ∂ Ω , in terms of a norm of u , a nonlinear potential of μ and the Wiener integral of 𝐑 n ∖ Ω . This quantifies the result on necessity of the Wiener criterion.