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2003 An existence result for nonlinear elliptic equations on $\Bbb R^d$ without sign condition
Yasuhiro Fujita
Differential Integral Equations 16(8): 969-979 (2003).

Abstract

In this paper, we consider the nonlinear elliptic equation of the following type: $$ -\frac{1}{2} \Delta u(x) + \nabla w(x)\cdot \nabla u(x) + [\lambda + H(x,u(x))]u(x) = f(x),\qquad x \in {\mathbb R}^d, $$ where $\lambda$ is a given constant and $f$, $H$, and $w$ are given functions, respectively. The derivative $\nabla w$ of the function $w$ is unbounded on ${\mathbb R}^d$. Our purpose is to show the existence of a solution to this equation without sign conditions on $H$. Therefore, we can treat even the case that $H$ is unbounded below on ${\mathbb R}^d$. This is due to the existence of the term $\nabla w\cdot \nabla u$.

Citation

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Yasuhiro Fujita. "An existence result for nonlinear elliptic equations on $\Bbb R^d$ without sign condition." Differential Integral Equations 16 (8) 969 - 979, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1030.35059
MathSciNet: MR1989596

Subjects:
Primary: 35J60

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 8 • 2003
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