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    Quasilinear elliptic problems interacting with its asymptotic spectrum

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    URI: http://hdl.handle.net/10835/580
    ISSN: 0362-546X
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    Author/s
    Arcoya, David; Carmona Tapia, José
    Date
    2003-03
    Abstract
    Under suitable assumptions on the coefficients of the matrix A(x,u) and on the nonlinear term f(x,u), we study the quasilinear problem in bounded domains Ω⊂RN−div(A(x,u)∇u)=f(x,u),x∈Ω,u=0,x∈∂Ω.We extend the semilinear results of Landesman–Lazer (J. Math. Mech. 19 (1970) 609) and of Ambrosetti–Prodi (in: A Primer on Nonlinear Analysis, Cambridge University Press, Cambridge, 1993) for resonant problems. The existence of positive solution is also considered extending to the quasilinear case the classical result by Ambrosetti–Rabinowitz (J. Funct. Anal. 14 (1973) 349). In this case, the result is obtained as a corollary of the previous multiplicity result in the Ambrosetti–Prodi framework. Keywords: Quasilinear elliptic equations; Bifurcation theory; Resonance; Jumping nonlinearities
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    Mathematics
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    • Artículos de revista Dpto. Matemáticas [118]

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