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Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains  [cached]
Zhiren Jin
Electronic Journal of Differential Equations , 2005,
Abstract: When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations that are similar either to the singular Emden-Fowler equation or a sublinear elliptic equation. The result obtained can be applied to equations with coefficients of the nonlinear term growing exponentially. The proof is based on the super and sub-solution method. A super solution itself is constructed by solving a quasilinear elliptic equation via a modified Perron's method.
Elliptic equations with discontinuous coefficients in unbounded domains of R^2
Mario Troisi,Antonio Vitolo
Le Matematiche , 1996,
Abstract: In this paper we are concerned with second order elliptic equations in unbounded domains Ω of R^2 . We establish existence and uniqueness theorems under the assumptions that the leading coefficients are bounded and measurable in Ω and satisfy a suitable condition at infinity.
Solvability of the Dirichlet problem in W^{2,p} for elliptic equations with discontinuous coefficients in unbounded domains
Loredana Caso,Paola Cavaliere,Maria Transirico
Le Matematiche , 2002,
Abstract: In this paper some W^{2, p}-estimates for the solutions of the Dirichlet problem for a class of elliptic equations with discontinuous coefficients in unbounded domains are obtained. As a consequence, an existence and uniqueness theorem for such a problem is proved.
Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of  [PDF]
Noureddine Zeddini
Abstract and Applied Analysis , 2006, DOI: 10.1155/aaa/2006/24307
Abstract: This paper deals with a class of nonlinear elliptic equations inan unbounded domain D of ℝn, n≥3, with a nonempty compact boundary, where the nonlinear term satisfies someappropriate conditions related to a certain Kato classK∞(D). Our purpose is to give some existence results andasymptotic behaviour for positive solutions by using the Greenfunction approach and the Schauder fixed point theorem.
Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of n
Noureddine Zeddini
Abstract and Applied Analysis , 2006,
Abstract: This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of n , n≥3 , with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class K ∞ ( D ) . Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point theorem.
Global boundedness of the fundamental solution of parabolic equations with unbounded coefficients  [PDF]
Esther Bleich
Mathematics , 2013,
Abstract: The purpose of this paper is to obtain an upper bound for the fundamental solution for parabolic Cauchy problem u'=Au, where A is a second order elliptic partial differential operator with unbounded coefficients such that its potential and the potential of the formal adjoint of the operator A are bounded from below.
Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains  [cached]
Venkataramanarao Raghavendra,Rasmita Kar
Electronic Journal of Differential Equations , 2009,
Abstract: In this study, we prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem $$displaylines{ Lu-mu u g_{1} + h(u) g_{2}= fquad hbox{in }Omega,cr u = 0quad hbox{on }partialOmega }$$ in a suitable weighted Sobolev space. Here the domain $Omegasubsetmathbb{R}^{n}$, $ngeq 3$, is not necessarily bounded, and $h$ is a continuous bounded nonlinearity. The theory is also extended for $h$ continuous and unbounded.
The Dirichlet Problem for elliptic equations in unbounded domains of the plane  [PDF]
Paola Cavaliere,Maria Transirico
Journal of Function Spaces and Applications , 2008, DOI: 10.1155/2008/872891
Abstract: In this paper we prove a uniqueness and existence theorem for the Dirichlet problem in W2,p for second order linear elliptic equations in unbounded domains of the plane. Here the leading coefficients are locally of class VMO and satisfy a suitable condition at infinity.
Non autonomous parabolic problems with unbounded coefficients in unbounded domains  [PDF]
Luciana Angiuli,Luca Lorenzi
Mathematics , 2014,
Abstract: Given a class of nonautonomous elliptic operators $\A(t)$ with unbounded coefficients, defined in $\overline{I \times \Om}$ (where $I$ is a right-halfline or $I=\R$ and $\Om\subset \Rd$ is possibly unbounded), we prove existence and uniqueness of the evolution operator associated to $\A(t)$ in the space of bounded and continuous functions, under Dirichlet and first order, non tangential homogeneous boundary conditions. Some qualitative properties of the solutions, the compactness of the evolution operator and some uniform gradient estimates are then proved.
Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domain
Paola Cavaliere,Maria Longobardi,Antonio Vitolo
Le Matematiche , 1996,
Abstract: In this paper we deal with the multiplication operator u ∈ W^{k,p} (Ω) → gu ∈ L^q (Ω), with g belonging to a space of Morrey type. We apply our results in order to establish an a-priori bound for the solutions of the Dirichlet problem concerning elliptic equations with discontinuous coefficients.
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