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Nodal solutions to nonlinear eigenvalue problems on time scales. (English) Zbl 1103.34006
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.

34B15Nonlinear boundary value problems for ODE
39A10Additive difference equations
Full Text: DOI
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