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Reaction-diffusion coupled inclusions with variable exponents and large diffusion

Simsen Jacson, Stefanello Simsen Mariza, Wittbold Petra

Opuscula Mathematica

2021

Vol. 41, no. 4

539--570

This work concerns the study of asymptotic behavior of coupled systems of p(x)-Laplacian differential inclusions. We obtain that the generalized semiflow generated by the coupled system has a global attractor, we prove continuity of the solutions with respect to initial conditions and a triple of parameters and we prove upper semicontinuity of a family of global attractors for reaction-diffusion systems with spatially variable exponents when the exponents go to constants greater than 2 in the topology of [formula] and the diffusion coefficients go to infinity.

Study of ODE limit problems for reaction-diffusion equations

Simsen J., Simsen M. S., Zimmermann A.

Opuscula Mathematica

2018

Vol. 38, no. 1

117--131

In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in [formula] and the diffusion coefficients go to infinity.

General mixed vector F-implicit complementarity problems in Banach spaces

Wu K.-Q., Huang N.-J.

Journal of Applied Analysis

2008

Vol. 14, nr 1

73-88

In this paper, we introduce a new class of general mixed vector F -implicit complementarity problems and general mixed vector F -implicit variational inequality problems, and study the equivalence between of them under certain assumptions in Banach spaces. We alsoderive some new existence theorems of solutions for the general lllixed vector F -implicit complementarity problems and the general mixed vector F -implicit variational inequality problems by using the FKKM theorem under some suitable assumptions without monotonicity. Moreover , we establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution mapping of the general mixed vector F -implicit variational inequality problems.

Existence conditions in symmetric multivalued vector quasiequilibrium problems

Anh L. Q., Khanh P. Q.

Control and Cybernetics

2007

Vol. 36, no 3

519-530

We consider symmetric multivalued vector quasiequilibrium problems in topological vector spaces. Sufficient conditions for the solution existence are established under relaxed assumptions, which are shown by examples to be essential, easy to check and more advantageous than recent known results. Applications to lower and upper bounded quasiequilibrium problems and to coincidence point problems are given.