Publishing house / Journals and Serials / Annales Polonici Mathematici / All issues

Abstract

Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations $$\cases{ \mathop{\rm div}(A(x)\|\nabla y\|^{p-1}\nabla y) +\langle\,b(x),\|\nabla y\|^{p-1}\nabla y\,\rangle+C(x,y)=e(x),\cr C(x,y)=c(x)|y|^{p-1}y+\sum\limits^m_{i=1}c_i(x)|y|^{p_i-1}y } $$ under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with mixed nonlinearities, and include some known oscillation results in the literature