American Institute of Mathematical Sciences

September  2009, 8(5): 1607-1618. doi: 10.3934/cpaa.2009.8.1607

Entire large solutions of semilinear elliptic equations of mixed type

 1 Department of Mathematics and Statistics, Air Force Institute of Technology/ ENC, 2950 Hobson Way, Wright Patterson AFB, OH 45433-7765, United States 2 Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, United States

Received  October 2008 Revised  January 2009 Published  April 2009

We prove existence and nonexistence of nonnegative entire large solutions for the semilinear elliptic equation $\Delta u = p(x)f(u) + q(x)g(u)$ in which $f$ and $g$ are nondecreasing and vanish at the origin. The locally Hölder continuous functions $p$ and $q$ are nonnegative. We extend results previously obtained for special cases of $f$ and $g$.
Citation: Alan V. Lair, Ahmed Mohammed. Entire large solutions of semilinear elliptic equations of mixed type. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1607-1618. doi: 10.3934/cpaa.2009.8.1607
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