Monotone methods for nonlinear boundary value problems in banach spaces

Bernfeld, Stephen R.; Lakshmikantham, V.

doi:10.1016/0362-546x(79)90020-8

Cited by 15 publications

(11 citation statements)

References 11 publications

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“…As usual, functions v, w ∈ C 2 ([0, 1], E) are called lower and upper solutions for problem (1) in case…”

Section: For I ⊆ ‫ޒ‬ (An Interval) a Function G : I × D → E Is Calledmentioning

confidence: 99%

Boundary Value Problems via an Intermediate Value Theorem

Herzog¹,

Lemmert²

2008

Glasgow Math. J.

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Abstract. We use an intermediate value theorem for quasi-monotone increasing functions to prove the existence of the smallest and the greatest solution of the Dirichlet problem u + f (t, u) = 0, u(0) = α, u(1) = β between lower and upper solutions, where f : [0, 1] × E → E is quasi-monotone increasing in its second variable with respect to a regular cone.2000 Mathematics Subject Classification. 34B15, 34C12, 34G20.

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“…As usual, functions v, w ∈ C 2 ([0, 1], E) are called lower and upper solutions for problem (1) in case…”

Section: For I ⊆ ‫ޒ‬ (An Interval) a Function G : I × D → E Is Calledmentioning

confidence: 99%

Boundary Value Problems via an Intermediate Value Theorem

Herzog¹,

Lemmert²

2008

Glasgow Math. J.

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“…These results are very important, in particular, for the method of lower and upper functions and the monotone iteration technique, which are efficient tools in proving the existence of solutions of various types for initial-value and boundary-value problems (see, e.g., [1][2][3][4][5][6] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Some remarks on linear functional differential inequalities of hyperbolic type

Šremr

2008

Ukr Math J

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“…These phenomena are modelled by stochastic processes s n n t called respectively the signal and noise processes. The signal cannot be observed directly; instead, at time / the sum (1) *t = s t + n t is observed. Roughly speaking, the filtering problem is to make a "best" estimate for s t given observations z T for times r < t. Closely related problems are to best estimate s T when t < T (the prediction problem) and for T < t (the data smoothing problem).…”

Section: Bulletin (New Seriesmentioning

confidence: 99%