| Abstrakt: |
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. |
