The exact number of solutions for the second order nonlinear boundary value problem |
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Authors: | Peter Somora |
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Institution: | (1) Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia |
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Abstract: | A second order nonlinear differential equation with homogeneous Dirichlet boundary conditions is considered. An explicit expression
for the root functions for an autonomous nonlinear boundary value problem is obtained using the results of the paper SOMORA,
P.: The lower bound of the number of solutions for the second order nonlinear boundary value problem via the root functions method, Math. Slovaca 57 (2007), 141–156]. Other assumptions are supposed to prove the monotonicity of root functions and to get the exact number
of solutions. The existence of infinitely many solutions of the boundary value problem with strong nonlinearity is obtained
by the root function method as well.
The paper was supported by the Grant VEGA No. 2/7140/27, Bratislava. |
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Keywords: | boundary value problem shooting method shooting function root function variational solution variational index |
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