Variational inequalities for energy functionals with nonstandard growth conditions.
Local and global integrability of gradients in obstacle problems.
Global Gradient Bounds for Relaxed variational problems.
Stability in Obstacle Problems.
The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.
In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λu = f(u), u ∈ H (Ω) in an exterior domain Ω = RO (N ≥ 3) with O a smooth bounded and star-shaped open set, and lim f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.
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