We describe the qualitative properties of the solutions of the second order scalar equation x'' + q(t)g(x) = 0, where q is a changing sign function, and consider the problem of existence and multiplicity of solutions which satisfy various different boundary conditions. In particular we outline some difficulties which arise in the use of the shooting approach.
Papini, D., Zanolin, F. (2002). Differential equations with indefinite weight: boundary value problems and qualitative properties of the solutions. In Turin Fortnight Lectures on Nonlinear Analysis (pp.265-295).
Differential equations with indefinite weight: boundary value problems and qualitative properties of the solutions
PAPINI, DUCCIO;
2002-01-01
Abstract
We describe the qualitative properties of the solutions of the second order scalar equation x'' + q(t)g(x) = 0, where q is a changing sign function, and consider the problem of existence and multiplicity of solutions which satisfy various different boundary conditions. In particular we outline some difficulties which arise in the use of the shooting approach.
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https://hdl.handle.net/11365/17439
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