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Nodal solutions of boundary value problems with boundary conditions involving Riemann–Stieltjes integrals

✍ Scribed by Jeremy Chamberlain; Lingju Kong; Qingkai Kong

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
232 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

We study the nonlinear boundary value problem consisting of the equation -y ′′ = ∑ m i=1 w i (t)f i (y) and a boundary condition involving a Riemann-Stieltjes integral. By relating it to the eigenvalues of the corresponding linear Sturm-Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. The shooting method and an energy function are used to prove the main results.

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