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

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.

The existence of multiple solutions u∈H10(Ω) to a differential inclusion of the type −Δu∈∂J(x,u) in Ω, where ∂J(x,⋅) denotes the generalized sub-differential of J(x,⋅), is investigated through critical point theorems for locally Lipschitz continuous functionals on closed convex sets of a Hilbert space.