A Note on the Singular Sturm-Liouville Problem with Infinitely Many Solutions
Southwest Texas State University, Department of Mathematics
We consider the Sturm-Liouville nonlinear boundary-value problem -u''(t) = α(t)ƒ(u(t)), 0 < t < 1, αu(0) - βu' (0) = 0, γu(1) + δu'(1) = 0, where α, β, γ, δ ≥ 0, αγ + αδ + βγ > 0 and a(t) is in a class of singular functions. Using a fixed point theorem we show that under certain growth conditions imposed on ƒ(u) the problem admits infinitely many solutions.
Sturm-Liouville problem, Green's function, Fixed point theorem, Holder's inequality, Multiple solutions
Kosmatov, N. (2002). A note on the singular Sturm-Liouville problem with infinitely many solutions. <i>Electronic Journal of Differential Equations, 2002</i>(80), pp. 1-10.