On nonhomogeneous elliptic equations with the Hardy-Leray potentials

Abstract

In this paper, we present some suitable distributional identities of the solutions for nonhomogeneous elliptic equations involving the Hardy-Leray potentials and study qualitative properties of the solutions to the corresponding nonhomogeneous problems by the distributional identities. We address some applications on the nonexistence of some nonhomogeneous problems with the Hardy-Leray potentials and the nonexistence principle eigenvalue with some indefinite potentials.

References in corpus (2)

• Elliptic Equations Involving Meausres
• Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential

Cited by in corpus (8)

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• Nonexistence of Positive Supersolution to a Class of Semilinear Elliptic Equations and Systems in an Exterior Domain
• Schr{ö}dinger operators with Leray-Hardy potential singular on the boundary
• Isolated singularities for elliptic equations with Hardy operator and source nonlinearity
• A note on the nonexistence of positive supersolutions to elliptic equations with gradient terms
• Positive supersolutions for the Lane-Emden system with inverse-square potentials
• The Poisson problem for the fractional Hardy operator: Distributional identities and singular solutions
• Solutions of nonhomogeneous equations involving Hardy potentials with singularities on the boundary