Geodesic
Destabilization for quasivariational inequalities of reaction-diffusion type
Applications of Mathematics, Tome 45 (2000) no. 3, pp. 161-176.

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We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
DOI : 10.1023/A:1023033910657
Classification : 35B35, 35J85, 35K57, 35K85, 47J20
Keywords: reaction-diffusion system; unilateral conditions; quasivariational inequality; Leray-Schauder degree; eigenvalue; stability 
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Babický, Vítězslav. Destabilization for quasivariational inequalities of reaction-diffusion type. Applications of Mathematics, Tome 45 (2000) no. 3, pp. 161-176. doi : 10.1023/A:1023033910657. http://geodesic.mathdoc.fr/articles/10.1023/A:1023033910657/

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