1,721,061 research outputs found
Diffusion-type operators, Liouville theorems and gradient estimates on complete manifolds
No full textWe study Liouville theorems and gradient estimates for solutions of Eq. (1.1) with the help of a diffusion operator and the related geometry
Entire solutions of singular elliptic inequalities on complete manifolds
Full text linkWe present some qualitative properties for solutions of singular quasilinear elliptic differential inequalities on complete Riemannian manifolds, such as the validity of the weak maximum principle at infinity, and non-existence results
The compact support principle for differential inequalities with gradient terms
No full textWe give some sufficient conditions to guarantee the validity of the Compact Support Principle for solutions of some singular elliptic differential inequalities on complete, non-compact manifolds. Our results apply in particular to the p-Laplace and the Mean Curvature operators. We also show that our results are sharp in many important cases
Strongly subharmonic functions, graphs, and their asymptotic growth
No full textLet G be an infinite connected graph with uniformly bounded vertex degree, and let denote the Laplace operator corresponding to the simple random walk on it. In this paper we obtain relations between the structure of the graph and the qualitative behaviour of the class of functions u satisfying ub>0, namely we relate the asymptotic growth of the function u and that of the cardinality of balls in G
Some remarks on the weak maximum principle
No full textWe obtain a maximum principle at infinity for solutions of a class of nonlinear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumptions of volume growth conditions. In the case of the Laplace-Beltrami operator we relate our results to stochastic completeness and parabolicity of the manifold
On weak solutions of nonlinear weighted p-Laplacian elliptic inequalities
No full textIn this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class of p-Laplacian elliptic inequalities with possibly singular weights. In order to get the results a new Omori–Yau type principle is used. We complement our nonexistence results by establishing existence of infinitely many positive radial solutions each of which blows up at some finite R>0. Finally, a criterium for the existence of positive entire large radial solutions of class is also established
“A priori” estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds
No full textAbstractWe study the asymptotic behaviour of non-negative solutions of Yamabe type equations on a complete Riemannian manifold. Then we provide a comparison result, based on a form of the weak maximum principle at infinity, which together with the “a priori” estimates previously obtained, yields uniqueness under very general Ricci assumptions. The paper ends with an existence result and an application to the non-compact Yamabe problem
Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary
No full textWe prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary (M,∂M,〈,〉) and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the so called Conformal Method
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