Existence of nodal solutions of a nonlinear eigenvalue problem with indefinite weight function. (English) Zbl 1173.34310

Ma, Ruyun; Han, Xiaoling

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 5-6, 2119-2125 (2009).

Summary: We investigate the existence of nodal solutions of the indefinite weight boundary value problem \[ u^{\prime \prime }+rh(t)f(u)= 0 , \quad 0 < t < 1,\qquad u(0)=u(1)=0, \] where \(h\in C\)[0,1] changes sign. The proof of our main result is based upon bifurcation techniques.

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34C23	Bifurcation theory for ordinary differential equations

Keywords:

indefinite weight; bifurcation; nodal solutions

References:

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