In this paper, we study the existence of solutions for a system of quadratic
integral equations of Chandrasekhar type by applying fixed point theorem of
a 2 x 2 block operator matrix defined on a nonempty bounded closed convex
subsets of Banach algebras where the entries are nonlinear operators.
In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].
AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$
∞
-Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.
Gerardy: Christian Ludwig Gerling an Carl Friedrich Gauss/Vainberg: Variational Methods for the Study of Nonlinear Operators/Zurmühl: Matrizen und ihre technischen Anwendungen/Bradford: Elementare Topologie/Petrow: Einstein-Räume/Weber: General Relativity
