Displaying similar documents to “Martin boundary and positive solutions of some boundary value problems”

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

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We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.

Reduction of a Schwartz-type boundary value problem for biharmonic monogenic functions to Fredholm integral equations

Serhii V. Gryshchuk, Sergiy A. Plaksa (2017)

Open Mathematics

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We consider a commutative algebra over the field of complex numbers with a basis e1, e2 satisfying the conditions [...] (e12+e22)2=0,e12+e22≠0. ( e 1 2 + e 2 2 ) 2 = 0 , e 1 2 + e 2 2 ≠ 0 . Let D be a bounded simply-connected domain in ℝ2. We consider (1-4)-problem for monogenic -valued functions Φ(xe1 + ye2) = U1(x, y)e1 + U2(x, y)i e1 + U3(x, y)e2 + U4(x, y)i e2 having the classic derivative in the domain Dζ = xe1 + ye2 : (x, y) ∈ D: to find a monogenic in Dζ function Φ, which is continuously extended to the boundary ∂Dζ, when...

Boundary properties of functions with finite Dirichlet integrals

J. L. Doob (1962)

Annales de l'institut Fourier

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L’auteur étudie dans un espace de Green (en particulier un domaine borné de R n ) les fonctions B L D (limites en un certain sens des fonctions assez régulières à intégrale de Dirichlet finie). On se ramène au cas harmonique montré qu’une telle fonction harmonique u est solution d’un problème de Dirichlet-Martin (c’est-à-dire correspond à une donnée u ' sur la frontière de Martin), ce qui entraîne l’existence d’une limite “fine” u ' p.p. Cela résulte de travaux antérieurs et de la remarque que...