Positive solutions of elliptic partial differential equations
نویسندگان
چکیده
منابع مشابه
On the Solutions of Quasi-linear Elliptic Partial Differential Equations*
The literature concerning these equations being very extensive, we shall not attempt to give a complete list of references. The starting point for many more modern researches has been the work of S. Bernstein,f who was the first to prove the analyticity of the solutions of the general equation with analytic and who was able to obtain a priori bounds for the second and higher derivatives of ...
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The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of their consequences. 2000 Mathematics Subject Classification. Primary 35J15; Secondary 35B05, 35C15, 35K10.
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where L is an elliptic differential operator of the second order, E is a bounded smooth 1 domain in R and ψ is a continuously differentiable positive function. Our goal is to describe the set U of all positive solutions of this equation. We say that an element u of U is moderate if u ≤ h for some h such that Lh = 0 in E. We say that u is σ-moderate if it is the limit of an increasing sequence o...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1968
ISSN: 0022-247X
DOI: 10.1016/0022-247x(68)90250-3