Integral Equations and Applications

Corduneanu, C.

doi:10.1017/cbo9780511569395

Cited by 500 publications

(297 citation statements)

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“…The initial condition (13) shows that trees that reach their maximum size have no commercial value: they just die out. The conditions (8) and (10) state that the discounted in situ value of a young tree should be equal to its planting cost along an interior optimal regime. Otherwise, it is profitable to plant more trees or not to plant at all.…”

Section: Optimality Conditionsmentioning

confidence: 99%

Optimal harvesting in forestry: steady-state analysis and climate change impact

Hritonenko

Yatsenko

Goetz

et al. 2013

Journal of Biological Dynamics

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We perform the steady-state analysis of a nonlinear partial differential equation model that describes the dynamics of a managed size-structured forest. The harvesting policy is to maximize the net benefits from timber production over an infinite planning horizon. The existence and uniqueness of the steady-state trajectories are analysed. Closed-form steady states are obtained in meaningful special cases and are used to estimate how climate change affects the optimal harvesting regime, diameter of cut trees, number of logged trees, and net benefits in the long run.

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Section: Optimality Conditionsmentioning

confidence: 99%

Optimal harvesting in forestry: steady-state analysis and climate change impact

Hritonenko

Yatsenko

Goetz

et al. 2013

Journal of Biological Dynamics

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“…Integral equations and inclusions occur in a natural way in the description of many physical phenomena; see the books by Corduneanu [14,15]. where a, b > 0, θ = (0, 0), ξ i , µ i ≥ 0, i = 1, .…”

Section: Introductionmentioning

confidence: 99%

Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay

Abbas¹,

Benchohra²

2013

OpMath

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“…The work can be introduced in three subsections. (1). By changes of variable, many equations will fit this form.…”

Section: Introductionmentioning

confidence: 99%

“…By changes of variable, many equations will fit this form. The general theory for (1) when V (t, x) = x and S is linear is found in Corduneanu [1].…”

Section: Introductionmentioning

confidence: 99%

Integral equations, implicit functions, and fixed points

Burton

1996

Proc. Amer. Math. Soc.

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Abstract. The problem is to show that (1) V (t, x) = S(t,t 0 H (t, s, x(s)) ds) has a solution, where V defines a contraction,Ṽ , and S defines a compact map,S. A fixed point of P ϕ =Sϕ + (I −Ṽ )ϕ would solve the problem. Such equations arise naturally in the search for a solution of f (t, x) = 0 where f(0, 0) = 0, but ∂f(0, 0)/∂x = 0 so that the standard conditions of the implicit function theorem fail. Now P ϕ =Sϕ + (I −Ṽ )ϕ would be in the form for a classical fixed point theorem of Krasnoselskii if I −Ṽ were a contraction. But I −Ṽ fails to be a contraction for precisely the same reasons that the implicit function theorem fails. We verify that I −Ṽ has enough properties that an extension of Krasnoselskii's theorem still holds and, hence, (1) has a solution. This substantially improves the classical implicit function theorem and proves that a general class of integral equations has a solution.

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Integral Equations and Applications

Cited by 500 publications

References 0 publications

Optimal harvesting in forestry: steady-state analysis and climate change impact

Optimal harvesting in forestry: steady-state analysis and climate change impact

Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay

Integral equations, implicit functions, and fixed points

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