Displaying similar documents to “Multiple solutions to a Cafarelli-Kohn-Nirenberg type equation with asymptotically linear term.”

Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations

Leszek Gęba, Tadeusz Pruszko (1991)

Annales Polonici Mathematici

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This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in Ω ⊂ ℝ n , u = D u = . . . = D m - 1 u on ∂Ω in the Sobolev space W 0 m , 2 ( Ω ) , where L is any selfadjoint strongly elliptic linear differential operator of order 2m. Using both topological degree arguments and minimax methods we obtain existence and multiplicity results for the above problem.

Location of the critical points of certain polynomials

Somjate Chaiya, Aimo Hinkkanen (2013)

Annales UMCS, Mathematica

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Let D¯ denote the unit disk {z : |z| < 1} in the complex plane C. In this paper, we study a family of polynomials P with only one zero lying outside D¯. We establish criteria for P to satisfy implying that each of P and P' has exactly one critical point outside D¯.

Positive solutions of nonlinear elliptic systems

Robert Dalmasso (1993)

Annales Polonici Mathematici

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We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, L ∞ a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.