an:00447070
Zbl 0785.34025
O'Regan, Donal
Solvability of some two-point boundary value problems of Dirichlet, Neumann or periodic type
EN
Dyn. Syst. Appl. 2, No. 2, 163-182 (1993).
00015353
1993
j
34B15
a priori bounds; two point boundary value problems; Dirichlet, Neumann or periodic type; nonlinear alternative of Leray-Schauder
The paper deals with the existence of solutions for two point boundary value problems \({1 \over p} (py')'=qf(t,y,py')\), \(0<t<1\), of Dirichlet, Neumann or periodic type. The tools are the nonlinear alternative of Leray-Schauder and the ``a priori bounds'' technique. The novelty is that the conditions ensuring the a priori boundedness of the solutions are expressed with the aid of a number \(c\) located between two consecutive eigenvalues of the problem: \({1 \over p} (py')'+\lambda y=0\), \(y\) satisfies the corresponding Dirichlet, Neumann or periodic boundary condition.
R.Precup (Cluj-Napoca)