Examinando por Autor "Arcoya, David"

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  • Miniatura
    Publicación
    Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian
    (2016-03-10) Arcoya, David; Colorado, Eduardo; Leonori, Tommaso; https://orcid.org/0000-0002-7284-2413; https://orcid.org/0000-0002-1067-5752; https://orcid.org/0000-0002-0848-4463
    This work deals with bifurcation of positive solutions for some asymptotically linear problems, involving the square root of the Laplacian (-Delta)(1/2). A simplified model problem is the following: {(-Delta)(1/2)u = lambda m(x)u + g(u) in Omega, u = 0 on partial derivative Omega, with Omega subset of R-N a smooth bounded domain, N >= 2, lambda > 0, m is an element of L-infinity(Omega), m(+) not equivalent to 0 and g is a continuous function which is super-linear at 0 and sub-linear at infinity. As a consequence of our bifurcation theory approach we prove some existence and multiplicity results. Finally, we also show an anti-maximum principle in the corresponding functional setting.
  • Miniatura
    Publicación
    Existence of solutions for semilinear nonlocal elliptic problems via a Bolzano theorem
    (Springer-Verlag, 2013-10-01) Arcoya, David; Leonori, Tommaso; Primo, Ana; https://orcid.org/0000-0002-7284-2413; https://orcid.org/0000-0002-0848-4463; https://orcid.org/0000-0003-1804-3175
    In this paper we deal with the existence of positive solutions for the following nonlocal type of problems {-Δu = α/(σωg(u)dx) p f(u) in Ω u>0 in Ω u=0 on ∂ Ω where Ω is a bounded smooth domain in ℝ N (N≥1), f,g are continuous positive functions, σ>0 and pεℝ. We give sufficient conditions on the functions f and g in order to have existence of positive solutions.