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Bensoussan, A., Baccordo, L. and Murat, F. (1988) On a nonlinear partial differential equation having natural growth terms and unbounded solution. Annales de l’institut Henri Poincaré (C) Analyse Non Linéaire, 5, 347-364.

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• 标题: 关于梯度具有一般增长的非线性椭圆问题有界解的存在性Existence of Bounded Solutions to a Class of Nonlinear Elliptic Problems with General Growth in the Gradient

  作者: 田玉娟, 马超

  关键字: 非线性椭圆方程, 梯度项, 有界解, 对称技术Nonlinear Elliptic Equation, Gradient Term, Bounded Solution, Symmetric Technique

  期刊名称: 《Pure Mathematics》, Vol.5 No.4, 2015-07-16

  摘要: 本文研究了一类关于梯度具有 增长的非线性椭圆方程。通过对一类Volterra型积分算子不动点的讨论，我们应用对称技术证明了有界解的存在性。 This paper studies a class of nonlinear elliptic equations with growth in the gra-dient. By discussing the fixed point for a class of Volterra integral operator, we use symmetric technique to prove the existence of bounded solutions.