We investigate two boundary value problems for the second order differential equation with p-Laplacian (a(t)P(x′))′ = b(t)F(x), t in I = [0,1), 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 x(t) = 0; ii) x′(0) = d < 0, lim x(t) = 0.

On some boundary value problems for second order nonlinear differential equations / M. Marini; S. Matucci; Z. Dosla. - In: MATHEMATICA BOHEMICA. - ISSN 0862-7959. - STAMPA. - 137:(2012), pp. 113-122.

On some boundary value problems for second order nonlinear differential equations

MARINI, MAURO;MATUCCI, SERENA;
2012

Abstract

We investigate two boundary value problems for the second order differential equation with p-Laplacian (a(t)P(x′))′ = b(t)F(x), t in I = [0,1), 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 x(t) = 0; ii) x′(0) = d < 0, lim x(t) = 0.
137
113
122
M. Marini; S. Matucci; Z. Dosla
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/373211
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