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On some boundary value problems for second order nonlinear differential equations

Zuzana Došlá, Mauro Marini, Serena Matucci (2012)

Mathematica Bohemica

We investigate two boundary value problems for the second order differential equation with p -Laplacian ( a ( t ) Φ p ( x ' ) ) ' = b ( t ) F ( x ) , t I = [ 0 , ) , 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 x ( t ) = 0 ; ii ) x ' ( 0 ) = d < 0 , lim t x ( t ) = 0 .

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