Differential and Integral Equations

Bifurcation of obstacle problems with inclusions follow from degree results for variational inequalities

Martin Väth

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It is shown that every result about a local degree and thus about bifurcation for variational inequalities (which is usually an obstacle problem) leads to a corresponding result for a problem in which the obstacle is modeled by inclusions instead of inequalities. Using recent results about variational inequalities, we obtain in particular bifurcation of stationary spatially nonhomogeneous solutions of a reaction-diffusion system with only Neumann conditions and obstacles modeled by inclusions, and results for an elliptic equation with inclusions about bifurcation strictly between certain eigenvalues and also bifurcation at eigenvalues without multiplicity assumptions.

Article information

Differential Integral Equations, Volume 26, Number 11/12 (2013), 1235-1262.

First available in Project Euclid: 4 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35K57: Reaction-diffusion equations 35J60: Nonlinear elliptic equations 35J88: Systems of elliptic variational inequalities [See also 35R35, 49J40] 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]


Väth, Martin. Bifurcation of obstacle problems with inclusions follow from degree results for variational inequalities. Differential Integral Equations 26 (2013), no. 11/12, 1235--1262. https://projecteuclid.org/euclid.die/1378327424

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