scholarly journals Maximum principle and existence of solutions for non necessarily cooperative systems involving Schrödinger operators

2008 ◽  
Vol 58 (5) ◽  
Author(s):  
H. Serag ◽  
A. Qamlo
Keyword(s):  
Maximum Principle ◽  
Existence Of Solutions ◽  
Schrödinger Operators ◽  
Sufficient Conditions ◽  
Cooperative Systems ◽  
Schrodinger Operators ◽  
The Maximum Principle ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient ◽  
Generalized Maximum Principle

AbstractIn this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (gf q-positivity) for non cooperative systems.

Necessary and sufficient conditions for optimal controls in viscous flow problems

1994 ◽  
Vol 124 (2) ◽  
pp. 211-251 ◽  
Author(s):  
H. O. Fattorini ◽  
S. S. Sritharan
Keyword(s):  
Maximum Principle ◽  
Viscous Flow ◽  
Sufficient Conditions ◽  
Optimal Controls ◽  
The Maximum Principle ◽  
Flow Problems ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Necessary And Sufficient ◽  
The Pontryagin Maximum Principle

A class of optimal control problems in viscous flow is studied. Main results are the Pontryagin maximum principle and the verification theorem for the Hamilton–Jacobi–Bellman equation characterising the feedback problem. The maximum principle is established by two quite different methods.

scholarly journals Two-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operators

2019 ◽  
Vol 31 (04) ◽  
pp. 1950012 ◽  
Author(s):  
Horia D. Cornean ◽  
Alessandro Michelangeli ◽  
Kenji Yajima
Keyword(s):  
Schrödinger Operators ◽  
Sufficient Conditions ◽  
Schrodinger Operators ◽  
Two Dimensional ◽  
Point Interactions ◽  
Wave Operators ◽  
Regular Type ◽  
Local Point ◽  
Embedded Eigenvalue ◽  
Necessary And Sufficient

We study the threshold behavior of two-dimensional Schrödinger operators with finitely many local point interactions. We show that the resolvent can either be continuously extended up to the threshold, in which case we say that the operator is of regular type, or it has singularities associated with [Formula: see text] or [Formula: see text]-wave resonances or even with an embedded eigenvalue at zero, for whose existence we give necessary and sufficient conditions. An embedded eigenvalue at zero may appear only if we have at least three centers. When the operator is of regular type, we prove that the wave operators are bounded in [Formula: see text] for all [Formula: see text]. With a single center, we always are in the regular type case.

scholarly journals Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ismail Kucuk ◽  
Kenan Yildirim
Keyword(s):  
Maximum Principle ◽  
Space Dimension ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Distributed Parameter ◽  
Hyperbolic Partial Differential Equation ◽  
The Maximum Principle ◽  
Convexity Assumptions ◽  
Necessary And Sufficient ◽  
One Space Dimension

The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. Pontryagin maximum principle is derived to be a necessary condition for the controls of such systems to be optimal. With the aid of some convexity assumptions on the constraint functions, it is obtained that the maximum principle is also a sufficient condition for the optimality.

scholarly journals Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators

2001 ◽  
Vol 27 (12) ◽  
pp. 725-736
Author(s):  
Laure Cardoulis
Keyword(s):  
Existence Of Solutions ◽  
Schrödinger Operators ◽  
Cooperative Systems ◽  
Fredholm Alternative ◽  
Schrodinger Operators ◽  
Limit Case ◽  
Cooperative System ◽  
Semilinear Systems ◽  
Existence Of A Solution

We study the existence of a solution for a non-necessarily cooperative system ofnequations involving Schrödinger operators defined onℝNand we study also a limit case (the Fredholm Alternative (FA)). We derive results for semilinear systems.

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

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