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Shuqin Zhang - One of the best experts on this subject based on the ideXlab platform.
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the Existence of a solution for a fractional differential equation with nonlinear boundary conditions considered using upper and lower solutions in reverse order
Computers & Mathematics With Applications, 2011Co-Authors: Shuqin ZhangAbstract:Using the method of upper and lower solutions in reverse order, we present an Existence Theorem for a linear fractional differential equation with nonlinear boundary conditions.
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Existence of a solution for the fractional differential equation with nonlinear boundary conditions
Computers & Mathematics With Applications, 2011Co-Authors: Shuqin ZhangAbstract:Using the method of upper and lower solutions and its associated monotone iterative, we present an Existence Theorem for a nonlinear fractional differential equation with nonlinear boundary conditions.
J Dai - One of the best experts on this subject based on the ideXlab platform.
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on unique Existence Theorem and exact solution formula of the inverse black body radiation problem
IEEE Transactions on Antennas and Propagation, 1992Co-Authors: X Dai, J DaiAbstract:The unique Existence Theorem of the inverse black-body radiation problem is proved. Its exact solution formula of closed form and some general Laurent expansions are derived. The Gaussian spectrum problem has been investigated numerically by many scientists, but its exact solution has not yet been obtained. The exact solution for the Gaussian spectrum problem is obtained by the derived exact solution formula and the criterion canceling divergence is described. >
Roger C E Tan - One of the best experts on this subject based on the ideXlab platform.
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double obstacle control problem for a quasilinear elliptic variational inequality with source term
Nonlinear Analysis-real World Applications, 2014Co-Authors: Qihong Chen, Delin Chu, Roger C E TanAbstract:Abstract In this paper, taking the double obstacle as the control variable, we consider an optimal control problem for a quasilinear elliptic variational inequality with source term. We establish the Existence Theorem and derive the optimality system for the underlying problem.
Frank Osterbrink - One of the best experts on this subject based on the ideXlab platform.
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Existence Theorem for Geometrically Nonlinear Cosserat Micropolar Model Under Uniform Convexity Requirements
Journal of Elasticity, 2015Co-Authors: Patrizio Neff, Mircea Bîrsan, Frank OsterbrinkAbstract:We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium system as a minimization problem. Applying the direct methods of the calculus of variations we show the Existence of minimizers. We present a clear proof based on the coercivity of the elastically stored energy density and on the weak lower semi-continuity of the total energy functional. Use is made of the dislocation density tensor $\overline{\boldsymbol{K}}= \overline{\boldsymbol{R}}^{T}\operatorname{Curl}\overline{\boldsymbol{R}}$ as a suitable Cosserat curvature measure.
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Existence Theorem for geometrically nonlinear cosserat micropolar model under uniform convexity requirements
arXiv: Analysis of PDEs, 2014Co-Authors: Patrizio Neff, Mircea Bîrsan, Frank OsterbrinkAbstract:We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium problem as a minimization problem. Applying the direct methods of the calculus of variations we show the Existence of minimizers. We present a clear proof based on the coercivity of the elastically stored energy density and on the weak lower semi-continuity of the total energy functional. Use is made of the dislocation density tensor $\bar{\boldsymbol{K}}=\bar{\boldsymbol{R}}^T\,\mathrm{Curl}\,\bar{\boldsymbol{R}}$ as a suitable Cosserat curvature measure.
K O Besov - One of the best experts on this subject based on the ideXlab platform.
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on balder s Existence Theorem for infinite horizon optimal control problems
Mathematical Notes, 2018Co-Authors: K O BesovAbstract:Balder’s well-known Existence Theorem (1983) for infinite-horizon optimal control problems is extended to the case in which the integral functional is understood as an improper integral. Simultaneously, the condition of strong uniform integrability (over all admissible controls and trajectories) of the positive part max{f0, 0} of the utility function (integrand) f0 is relaxed to the requirement that the integrals of f0 over intervals [T, T′] be uniformly bounded above by a function ω(T, T′) such that ω(T, T′) → 0 as T, T′→∞. This requirement was proposed by A.V. Dmitruk and N.V. Kuz’kina (2005); however, the proof in the present paper does not follow their scheme, but is instead derived in a rather simple way from the auxiliary results of Balder himself. An illustrative example is also given.
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on balder s Existence Theorem for infinite horizon optimal control problems
arXiv: Optimization and Control, 2017Co-Authors: K O BesovAbstract:Balder's well-known Existence Theorem (1983) for infinite-horizon optimal control problems is extended to the case when the integral functional is understood as an improper integral. Simultaneously, the condition of strong uniform integrability (over all admissible controls and trajectories) of the positive part $\max\{f_0,0\}$ of the utility function (integrand) $f_0$ is relaxed to the requirement that the integrals of $f_0$ over intervals $[T,T']$ be uniformly bounded from above by a function $\omega(T,T')$ such that $\omega(T,T')\to 0$ as $T,T'\to\infty$. This requirement was proposed by A.V. Dmitruk and N.V. Kuz'kina (2005); however, the proof in the present paper does not follow their scheme but is instead derived in a rather simple way from the auxiliary results of Balder himself. An illustrative example is also given.