Differential and Integral Equations

Existence results for some functional elliptic equations

Michel Chipot and Prosenjit Roy

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We consider nonlocal elliptic boundary value problems of the form $$ -\mathcal{A}(x,u) \bigtriangleup u = \lambda f(u) $$ with Dirichlet boundary conditions. We show that if $f$ has $n$ loops, then the problem has at least $n$ distinct solutions, by using very simple comparison principles. Also, we study the asymptotic behavior of such solutions as the parameter $\lambda $ tends to $\infty$.

Article information

Differential Integral Equations, Volume 27, Number 3/4 (2014), 289-300.

First available in Project Euclid: 30 January 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J15: Second-order elliptic equations 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations


Chipot, Michel; Roy, Prosenjit. Existence results for some functional elliptic equations. Differential Integral Equations 27 (2014), no. 3/4, 289--300. https://projecteuclid.org/euclid.die/1391091367

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