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
DOI: 10.12677/PM.2015.54022, PDF,    科研立项经费支持
作者: 田玉娟*：山东师范大学数学科学学院，山东 济南；马 超：济南大学数学科学学院，山东 济南
关键词: 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
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。
Abstract: 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.
文章引用：田玉娟, 马超. 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[J]. 理论数学, 2015, 5(4): 143-149. https://dx.doi.org/10.12677/PM.2015.54022

参考文献

[1] 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.
[2] Baccordo, L., Murat, F. and Puel, J.P. (1984) Résultats d'existence pour certains problèmes elliptiques quasilinéaires. Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze, 11, 213-285.
[3] Baccordo, L., Murat, F. and Puel, J.P. (1988) Existence of bounded solution for nonlinear elliptic unilateral problems, Annali di Ma-tematica Pura ed Applicata, 152, 183-196. http://dx.doi.org/10.1007/BF01766148 [Google Scholar] [CrossRef] 
[4] Baccordo, L., Murat, F. and Puel, J.P. (1992) estimate for some nonlinear elliptic partial differential equation and application to an existence result. SIAM Journal on Mathematical Analysis, 23, 326-333. http://dx.doi.org/10.1137/0523016 [Google Scholar] [CrossRef] 
[5] Ferone, V., Posteraro, M.R. and Rakotoson, J.M. (1999) -estimate for nonlinear elliptic problems with p-growth in the gradient. Journal of Inequalities and Applications, 3, 109-125. http://dx.doi.org/10.1155/s1025583499000077 [Google Scholar] [CrossRef] 
[6] Grenon, N. (2001) Existence and comparison results for qua-silinear elliptic equations with critical growth in the gradient. Journal of Differential Equations, 171, 1-23. http://dx.doi.org/10.1006/jdeq.2000.3833 [Google Scholar] [CrossRef] 
[7] Grenon, N. and Trombetti, C. (2003) Existence results for a class of nonlinear elliptic problems with p-growth in the gradient. Nonlinear Analysis: Theory, Methods & Applications, 52, 931-942. http://dx.doi.org/10.1016/S0362-546X(02)00143-8 [Google Scholar] [CrossRef] 
[8] Messano, B. (2006) Symmetrization results for classes of nonlinear elliptic equations with q-growth in the gradient. Nonlinear Analysis: Theory, Methods & Applications, 64, 2688-2703. http://dx.doi.org/10.1016/j.na.2005.07.042 [Google Scholar] [CrossRef] 
[9] Ferone, V. and Messano, B. (2007) Comparison and existence results for classes of nonlinear elliptic equations with general growth in the gradient. Advanced Nonlinear Studies, 7, 31-46.
[10] Kawohl, B. (1985) Rearrangement and convexity of level sets in PDE. Lecture Notes in Math., 1150, Springer-Verlag, Berlin.
[11] Pašić, M. (1996) Isoperimetric inequalities in quasilinear elliptic equations of Le-ray-Lions type. Journal de Mathématiques Pures et Appliqués, 75, 343-366.

为你推荐