Existence of Extremal Solutions of Singular Functional Cauchy and Cauchy–Nicoletti Problems

S. Seikkala () and S. Heikkilä ()
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S. Seikkala: University of Oulu
S. Heikkilä: University of Oulu

Chapter 27 in Integral Methods in Science and Engineering, Volume 1, 2010, pp 291-300 from Springer

Abstract: Abstract In this chapter we apply fixed point results for mappings in partially ordered spaces presented in ([CaHe00], [HeiLa94]) to derive existence results for the Cauchy problem $$q(u(t))u^\prime (t) = f(t,u) \mbox{for a.e} t \in J = [0, T], u(0) = 0,$$ and for the Cauchy-Nicoletti problem $$q_i(u_i(t))u_i^\prime (t) = f_i(t,u) \mbox{for a.e} t \in J, u_i(t_i) = c_i, i = 1, \ldots, n,$$ where $$0 = t_1

Date: 2010
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DOI: 10.1007/978-0-8176-4899-2_27

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