Quasilinear elliptic problems in unbounded domains

1973 ◽  
Vol 334 (1598) ◽  
pp. 397-410 ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Unbounded Domains ◽  
Elliptic Type ◽  
Quasilinear Elliptic Problems ◽  
Monotonicity Conditions ◽  
New Feature ◽  
Quasilinear Elliptic ◽  
Quasilinear Partial Differential Equation

This paper provides an existence theorem for the Dirichlet problem for a quasilinear partial differential equation of elliptic type in an unbounded domain. The principal new feature of this work is that the results are obtained under weaker monotonicity conditions on the coefficients of the equation than those employed in earlier work in this area.

scholarly journals Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

2005 ◽  
Vol 2005 (6) ◽  
pp. 607-617 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Parabolic Partial Differential Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

Modified Boundary Value Problems For a Quasi-Linear Elliptic Equation

1956 ◽  
Vol 8 ◽  
pp. 203-219 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Continuous Function ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Linear Elliptic Equation ◽  
Partial Differential

1. Introduction. The quasi-linear elliptic partial differential equation to be studied here has the form(1.1) Δu = − F(P,u).Here Δ is the Laplacian while F(P,u) is a continuous function of a point P and the dependent variable u. We shall study the Dirichlet problem for (1.1) and will find that the usual formulation must be modified by the inclusion of a parameter in the data or the differential equation, together with a further numerical condition on the solution.

scholarly journals Positive solutions of critical quasilinear elliptic problems in general domains

1998 ◽  
Vol 3 (1-2) ◽  
pp. 65-84 ◽  
Author(s):  
Filippo Gazzola
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Critical Growth ◽  
Quasilinear Elliptic Equations ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.

Non-Uniqueness of The Solution to a Generalized Dirichlet Problem

1974 ◽  
Vol 17 (4) ◽  
pp. 605-606
Author(s):  
E. L. Koh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Unique Solution ◽  
Partial Differential ◽  
Uniqueness Of The Solution ◽  
Image Position ◽  
Generalized Dirichlet

It is generally known [1] that the singular partial differential equationmay not have a unique solution because of the existence of nontrivial representations of zero.1

Electrostatics in a gravitational field

1978 ◽  
Vol 80 (3-4) ◽  
pp. 201-211 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Gravitational Field ◽  
Closed Form ◽  
Electrostatic Potential ◽  
Point Charge ◽  
Elementary Solution ◽  
Elliptic Type ◽  
Partial Differential

SynopsisIn this paper, the electrostatic potential of a point charge in a Reisser-Nordström gravitational field is found in closed form by using the theory of Hadamard's elementary solution of a partial differential equation of elliptic type.

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