On the oscillation of forced second order mixed-nonlinear elliptic equations

Zhiting Xu¹

¹ School of Mathematical Sciences South China Normal University Guangzhou, 510631, P.R. China

Annales Polonici Mathematici, Tome 98 (2010) no. 2, pp. 169-188

Résumé

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

Détail

DOI : 10.4064/ap98-2-5

Keywords: oscillation theorems established forced second order mixed nonlinear elliptic differential equations cases mathop div nabla p nabla langle nabla p nabla rangle p sum limits i under quite general conditions these results extensions recent results sun wong math anal appl zheng wang han appl math lett forced second order ordinary differential equations mixed nonlinearities include known oscillation results literature