Isolated singularities in semilinear problems
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This article is published in Journal of Differential Equations.The article was published on 1980-12-01 and is currently open access. It has received 157 citations till now.read more
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Global and local behavior of positive solutions of nonlinear elliptic equations
Basilis Gidas,Joel Spruck +1 more
Book
Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
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Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: Elliptic equations and systems
TL;DR: In this article, a general method for derivation of universal, pointwise, a priori estimates of local solutions from Liouville-type theorems, which provides a simpler and unified treatment for such questions, is presented.
Journal ArticleDOI
A probabilistic approach to one class of nonlinear differential equations
TL;DR: In this article, the authors established connections between positive solutions of one class of nonlinear partial differential equations and hitting probabilities and additive functionals of superdiffusion processes, and improved results on superprocesses by using the recent progress in the theory of removable singularities for differential equations.
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Local and global behavior of solutions of quasilinear equations of Emden-Fowler type
TL;DR: In this article, the authors considered the problem of finding non-radial positive solutions when q < N(p −1)/(N − p), and gave a complete classification of local and global radial solutions of any sign, for any q.
References
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Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
TL;DR: A survey of nonlinear functional analysis in ordered Banach spaces can be found in this paper, where some of the most important methods and results of non-linear functional analyses are discussed.
Journal ArticleDOI
Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
TL;DR: In this article, continuation and variational methods are developed to construct positive solutions for nonlinear elliptic eigenvalue problems, which contain models arising in chemical kinetics, nonlinear heat generation, and the gravitational equilibrium of polytropic stars.
Book ChapterDOI
Partial Differential Equations Invariant under Conformal or Projective Transformations
Charles Loewner,Louis Nirenberg +1 more
TL;DR: In this article, a Riemannian metric is defined in terms of a solution of the boundary value problem for a positive, strictly concave function u defined in Ω.
Journal ArticleDOI
Removable singularities in Yang-Mills fields
TL;DR: In this paper, it was shown that a field satisfying the Yang-Mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite.
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Global and local behavior of positive solutions of nonlinear elliptic equations
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