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Multiple solutions to elliptic inclusions via critical point theory on closed convex sets

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  • The existence of multiple solutions $u\in H^1_0(\Omega)$ to a differential inclusion of the type $-\Delta u\in \partial J(x,u)$ in $\Omega$, where $\partial J(x,\cdot)$ denotes the generalized sub-differential of $J(x,\cdot)$, is investigated through critical point theorems for locally Lipschitz continuous functionals on closed convex sets of a Hilbert space.
    Mathematics Subject Classification: Primary: 58E05, 49J35; Secondary: 49J57.


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