Nonlinear eigenvalue problems on a half-line and some related topics

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Abstract

The nonlinear eigenvalue problem

$-\left(\left|u^{\prime}(x)\right|^{p-1} \operatorname{sgn} u^{\prime}(x)\right)^{\prime}+(p-1) \omega(x)|u(x)|^{q-1} \operatorname{sgn} u(x)=(p-1) \lambda|u(x)|^{p-1} \operatorname{sgn} u(x), \quad 0 \leq x<\infty,$

for fixed p > q > 1, was studied under some conditions on the positive potential ω. We used various Prüfer angle methods to characterize the eigenvalue properties for problems on the half-line and finite intervals.

Keywords

nonlinear Sturm-Liouville equation / Prüfer angle method

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