Singular Dirichlet boundary value problems. II: Resonance case

Donal O'Regan

Displaying similar documents to “Singular Dirichlet boundary value problems. II: Resonance case”

Differential equations at resonance

Donal O'Regan (1995)

Commentationes Mathematicae Universitatis Carolinae

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New existence results are presented for the two point singular “resonant” boundary value problem $\frac{1}{p} {(p y^{'})}^{'} + r y + λ_{m} q y = f (t, y, p y^{'})$ a.eȯn $[0, 1]$ with $y$ satisfying Sturm Liouville or Periodic boundary conditions. Here $λ_{m}$ is the ${(m + 1)}^{s t}$ eigenvalue of $\frac{1}{p q} [{(p u^{'})}^{'} + r p u] + λ u = 0$ a.eȯn $[0, 1]$ with $u$ satisfying Sturm Liouville or Periodic boundary data.

Exponential stability of two coupled second-order evolution equations.

Wan, Qian, Xiao, Ti-Jun (2011)

Advances in Difference Equations [electronic only]

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Criteria for disfocality and disconjugacy for third order differential equations.

Panigrahi, S. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: $inf_{(u, v) \in 𝒰_{a d}} \int_{0}^{1} f (t, u (θ_{v} (t)), u^{'} (t), v (t)) d t$ , (1) where $𝒰_{a d}$ is a set of admissible controls and $θ_{v}$ is the solution of the following equation: ${\frac{d θ (t)}{d t} = g (t, θ (t), v (t)), t \in [0, 1]$ ; $θ (0) = θ_{0}, θ (t) \in [0, 1] \forall t$ . (2). The results are nonlocal and new.

Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition

Dana Říhová-Škabrahová (2001)

Applications of Mathematics

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The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part $Γ_{1}$ of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and...