1,721,071 research outputs found
Central Configurations of the N-Body Problem via the Equivariant Morse Theory
No full textPacella, Filomena. (1984). Central Configurations of the N-Body Problem via the Equivariant Morse Theory. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/2104
The topological degree for noncompact operators in Banach spaces with strictly convex duals
No full textAn extension of the topological degree theory is presente
Uniqueness of positive solutions of semilinear elliptic equations and related eigenvalue problems
No full textIn this paper we survey some recent results about the uniqueness of the solution of some semilinear elliptic Dirichlet problems in bounded domains. The presentation aims to emphasize the role of the geometrical properties of the second eigenfunction of the linearized problem in the study of the above question. This motivates the analysis of the asymptotic behaviour of these eigenfunctions and of the relative eigenvalues when the nonlinear term is a power with exponent close to the critical Sobolev exponent. © 2005 Birkhäuser Verlag, Basel/Switzerland
Note on spectral theory of nonlinear operators: extensions of some surjectivity theorems of Fuv cík and Nev cas
No full text
Symmetry properties of positive solutions of nonlinear differential equations involving the p-Laplace operator
No full textSymmetry results for solutions of semilinear elliptic equations with convex nonlinearities
No full textAbstractIn this paper, we study the symmetry properties of the solutions of the semilinear elliptic problem {−Δu=f(x,u)in Ωu=g(x)on ∂Ω, where Ω is a bounded symmetric domain in RN, N⩾2, and f:Ω×R→R is a continuous function of class C1 in the second variable, g is continuous and f and g are somehow symmetric in x. Our main result is to show that all solutions of the above problem of index one are axially symmetric when Ω is an annulus or a ball, g≡0 and f is strictly convex in the second variable. To do this, we prove that the nonnegativity of the first eigenvalue of the linearized operator in the caps determined by the symmetry of Ω is a sufficient condition for the symmetry of the solution, when f is a convex function
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