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Solutions to a perturbed critical semilinear equation concerning the N -Laplacian in N

Elliot Tonkes (1999)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the N -Laplacian - Δ N u - div ( | u | N - 2 u ) = e ( x , u ) + h ( x ) in Ω where u W 0 1 , N ( N ) , Ω is a bounded smooth domain in N , N 2 , e ( x , u ) is a critical nonlinearity in the sense of the Trudinger-Moser inequality and h ( x ) ( W 0 1 , N ) * is a small perturbation.

Solvability for semilinear PDE with multiple characteristics

Alessandro Oliaro, Luigi Rodino (2003)

Banach Center Publications

We prove local solvability in Gevrey spaces for a class of semilinear partial differential equations. The linear part admits characteristics of multiplicity k ≥ 2 and data are fixed in G σ , 1 < σ < k/(k-1). The nonlinearity, containing derivatives of lower order, is assumed of class G σ with respect to all variables.

Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations

Peter Poláčik (2002)

Mathematica Bohemica

We consider three types of semilinear second order PDEs on a cylindrical domain Ω × ( 0 , ) , where Ω is a bounded domain in N , N 2 . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of Ω × ( 0 , ) is reserved for time t , the third type is an elliptic equation with a singled out unbounded variable t . We discuss the asymptotic behavior, as t , of solutions which are defined and bounded on Ω × ( 0 , ) .

Currently displaying 1101 – 1120 of 1372