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Zbl 1103.34006
Luo, Hua; Ma, Ruyun
Nodal solutions to nonlinear eigenvalue problems on time scales. (English)
[J] Nonlinear Anal., Theory Methods Appl. 65, No. 4, A, 773-784 (2006). ISSN 0362-546X

Summary: Using global bifurcation theory, we obtain the existence of solutions with specified numbers of simple generalized zeros for the nonlinear eigenvalue problem on time scales $\bbfT$ $$-u^{\Delta\Delta}(t)+q(t)u^\sigma(t)= rf\bigl( u^\sigma(t)\bigr),\quad t\in\bbfT,\quad u(0)=u(1)=0,$$ where $r>0$ is a given constant. In addition, we argue that our existence theorem is a generalization of a previous result which shows the existence of at least one positive solution for the above problem.

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
39A10 Difference equations

Keywords: eigenvalue problems on time scales; multiplicity; bifurcation methods; simple generalized zeros

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