We consider the second order differential equation
x" = f(t,x,x'),
where f is a Carathéodory function. We prove the existence of at least one solution of the equation satisfying the nonlinear boundary conditions
g1(x(a),x'(a)) = 0, g2(x(b),x'(b)) = 0.
Our methods of proofs are based on the topological degree arguments for auxiliary operator equation.
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Vol. 10 (1996)
Published: 1996-09-30
10.1515/amsil
English