We study the existence of positive solutions for the nonlinear Schrödinger equation with the fractional LaplacianFurthermore, we analyse the regularity, decay and symmetry properties of these solutions.
We study uniformly elliptic fully nonlinear equations of the type F (D 2 u, Du, u, x) = f (x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects; we obtain existence and uniqueness results for nonproper operators whose principal eigenvalues (in some cases, only one of them) are positive; finally, we obtain an existence result for nonproper Isaac's equations.
Artículo de publicación ISIThe purpose of this paper is to study boundary blow up solutions for semi-linear fractional elliptic equations of the form
{(-Delta)(alpha)u(x) + vertical bar u vertical bar(p-1)u(x) = f(x), x is an element of Omega,
u(x) = 0, x is an element of(Omega) over bar (c)
lim(x is an element of Omega, x ->partial derivative Omega) u(x) = +infinity, where p > 1, Omega is an open bounded C-2 domain of R-N, N >= 2, the operator (-Delta)(alpha) with alpha is an element of (0, 1) is the fractional Laplacian and f: Omega -> R is a continuous function which satisfies some appropriate conditions. We obtain that problem (0.1) admits a solution with boundary behavior like d(x)(-2 alpha/p-1), when 1 + 2 alpha < p < 1 - 2 alpha/tau(0)(alpha), for some tau(0)(alpha) is an element of (-1, 0), and has infinitely many solutions with boundary behavior like d(x)(tau o(alpha)), when max{1 - 2 alpha/tau(0) + tau(0)(alpha)+1/tau(0), 1} < p < 1 - 2 tau/tau(0). Moreover, we also obtained some uniqueness and non-existence results for problem (0.1).CONICYT
FONDECYT
1110291
1110210
Programa BASALCMM U. de Chile
Programa BASAL-CMM U. de Chil
In this article we study some results on the existence of radially symmetric, non-negative solutions for the nonlinear elliptic equationHere N 3, p > 1 and M + λ, denotes the Pucci's extremal operators with parameters 0 < λ . The goal is to describe the solution set in function of the parameter p.
In this paper we extend existing results concerning generalized eigenvalues of Pucci's extremal operators. In the radial case, we also give a complete description of their spectrum, together with an equivalent of Rabinowitz's Global Bifurcation Theorem. This allows us to solve equations involving Pucci's operators.
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