On the singular second-order elliptic equation

Second-Order Elliptic Equation with Singularities

“…Such problem arises from various fields of geometry and physics. ere are many results for second-order elliptic equations, but most of them are focused on bounded domains Ω of R n or on compact Riemannian manifold (M, g), see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] for a survey. A variety of techniques have been used to solve second-order equations, and variational methods are the most suitable.…”

“…A famous result concerning the equation of type (1) has been obtained in [17], and it consists of the classification of positive solutions of the equation…”

“…􏽱 . e singular term a was introduced as follows: in [11], Madani studied equation (1) with f is a constant, a � (n − 2)/4(n − 1)S g , and such that the metric g admits a finite number of points with singularities and is smooth outside these points.…”

“…In [1] Azaiz et al studied some singular second-order elliptic equations. ey focused on the following equation:…”

“…In particular, in eorem 1.1, under additional assumptions, they proved the existence of λ * > 0 such that, for any λ ∈ (0, λ * ), the equation has a nontrivial weak solution. For details, see [1] and the references therein.…”