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Du, Y.* ; Efendiyev, M.A.

Existence and exact multiplicity for quasilinear elliptic equations in quarter-spaces.

In: Springer Proceedings in Mathematics and Statistics (Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 25-29 July 2016, Berlin). 2017. 128-137 ( ; 205)
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We consider positive solutions of quasilinear elliptic problems of the form Δpu+ f(u) = 0 over the quarter-space Q= { x∈ RN: x1> 0, x2> 0 }, with u= 0 on ∂Q. For a general class of nonlinearities f≥ 0 with finitely many positive zeros, we show that, for each z> 0 such that f(z) = 0, there is a bounded positive solution satisfying(Forumala Presented). where V is the unique solution of the one-dimensional problem (Forumala Presented). When p= 2, we show further that such a solution is unique, and there are no other types of bounded positive solutions to the quarter-space problem. Thus in this case the number of bounded positive solutions to the quarter-space problem is exactly the number of positive zeros of f.
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Publikationstyp Artikel: Konferenzbeitrag
Schlagwörter Asymptotic Behavior ; P-laplacian Equation ; Positive Solution ; Quarter-space
ISBN 978-3-319-64172-0
Konferenztitel Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday
Konferzenzdatum 25-29 July 2016
Konferenzort Berlin
Konferenzband Springer Proceedings in Mathematics and Statistics
Quellenangaben Band: 205, Heft: , Seiten: 128-137 Artikelnummer: , Supplement: ,
Begutachtungsstatus