Mauro Marini, Serena Matucci, Department of Electronic and Telecommunications, University of Florence, I-50139 Florence, Italy, e-mail: mauro.marini@
unifi.it, serena.matucci@unifi.it; Zuzana Došlá, Department of Mathematics and Statistics, Masaryk University, 61137 Brno, Czech Republic, e-mail: dosla@math.muni.cz
Abstract: We investigate two boundary value problems for the second order differential equation with $p$-Laplacian
(a(t)\Phi_p(x'))'=b(t)F(x), \quad t\in I=[0,\infty),
where $a$, $b$ are continuous positive functions on $I$. We give necessary and sufficient conditions which guarantee the existence of a unique (or at least one) positive solution, satisfying one of the following two boundary conditions:
i) x(0)=c>0, \lim_{t\rightarrow\infty}x(t)=0; \quad ii) \^^Mx'(0)=d<0, \lim_{t\rightarrow\infty}x(t)=0.
Keywords: boundary value problem, $p$-Laplacian, half-linear equation, positive solution, uniqueness, decaying solution, principal solution
Classification (MSC 2010): 34C10
Full text available as PDF.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
