Topological degree methods in BVPS with nonlinear conditions
Abstract
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.
Keywords
second order ordinary differential equation; nonlinear boundary value conditions; existence; topological degree
References
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6. I. Rachůnková, Sign conditions in nonlinear boundary value problems, Acta UP Olomuc., Fac. rer. nat. 114, Math. 33 (1994), 117-124.
Department of Mathematics, Faculty of Science, Palacký Univeristy, Czech Republic Czechia
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