Saddle point solutions for non-local elliptic operators
Keywords
Integrodifferential operators, fractional Laplacian, variational techniques, Saddle Point Theorem, Palais-Smale conditionAbstract
The paper deals with equations driven by a non-local integrodifferential operator $\mathcal L_K$ with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a solution for them using the Saddle Point Theorem. We prove this result for a general integrodifferential operator of fractional type and from this, as a particular case, one can derive an existence theorem for the fractional Laplacian, finding solutions of the equation $$ \begin{cases} (-\Delta)^s u=f(x,u) & {\mbox{in }} \Omega,\\ u=0 & {\mbox{in }} \mathbb{R}^n\setminus \Omega, \end{cases} $$ where the nonlinear term $f$ satisfies a linear growth condition.Downloads
Published
2016-04-12
How to Cite
1.
FISCELLA, Alessio. Saddle point solutions for non-local elliptic operators. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 44, no. 2, pp. 527 - 538. [Accessed 2 November 2024].
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