Displaying similar documents to “Critical nonlinear elliptic equations with singularities and cylindrical symmetry”

The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.

Gongbao Li, Gao-Feng Zheng (2006)

Revista Matemática Iberoamericana

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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.

Mapping properties of the elliptic maximal function.

M. Burak Erdogan (2003)

Revista Matemática Iberoamericana

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We prove that the elliptic maximal function maps the Sobolev space W4,eta(R2) into L4(R2) for all eta > 1/6. The main ingredients of the proof are an analysis of the intersectiQn properties of elliptic annuli and a combinatorial method of Kolasa and Wolff.

Perturbing plane cruve singularities.

Eduardo Casas-Alvero, Rosa Peraire (2003)

Revista Matemática Iberoamericana

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We describe the singularity of all but finitely-many germs in a pencil generated by two germs of plane curve sharing no tangent.