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We prove boundary asymptotics to solutions of weighted p-Laplacian equations that take infinite value on the boundary of a bounded domain. Uniqueness of such solutions would then follow as a… (More)
Abstract Given a bounded domain Ω we consider local weak blow-up solutions to the equation Δpu=g(x)f(u) on Ω . The non-linearity f is a non-negative non-decreasing function and the weight g is a… (More)
Abstract Under appropriate conditions on ƒ(x, t), we prove the existence of viscosity solutions to Δ∞ u = ƒ(x, u) that take prescribed continuous data on the boundary of bounded domains. As an… (More)
Abstract We consider the elliptic system Δ u = u a v b , Δ v = u c v d where the exponents are non-negative spherically symmetric functions. We study positive solutions on balls of finite and… (More)
Our purpose in this paper is to provide a self contained account of the inhomogeneous Dirichlet problem $\Delta_\infty u=f(x,u)$ where $u$ takes a prescribed continuous data on the boundary of… (More)
We prove existence and nonexistence of nonnegative entire large solutions for the semilinear elliptic equation $\Delta u = p(x)f(u) + q(x)g(u)$ in which $f$ and $g$ are nondecreasing and vanish at… (More)
Abstract We prove the existence of a ground state solution for the semi-linear elliptic equation − Δ u = f ( x , u ) on R N under suitable conditions on a locally Holder continuous non-linearity f (… (More)
We prove Harnack's inequality for non-negative solutions of some degenerate elliptic operators in divergence form with the lower order term coefficients satisfying a Kato type contition.
In this thesis we study some complex and hypercomplex function spaces and classes such as hypercomplex Besov spaces, Bloch space and Qp spaces as well as the class of basic sets of polynomials in… (More)