Abstract
This paper investigates the -Laplacian equations with singular nonlinearities in , on , where is called -Laplacian. The existence of positive solutions is given, and the asymptotic behavior of solutions near boundary is discussed.
Highlights
The study of differential equations and variational problems with nonstandard p(x)growth conditions is a new and interesting topic
In [4, 7], Fan and Zhao give the regularity of weak solutions for differential equations with nonstandard p(x)-growth conditions
We consider the p(x)-Laplacian equations with singular nonlinearities:
Summary
The study of differential equations and variational problems with nonstandard p(x)growth conditions is a new and interesting topic. In [4, 7], Fan and Zhao give the regularity of weak solutions for differential equations with nonstandard p(x)-growth conditions. On the existence of solutions for p(x)-Laplacian problems in bounded domain, we refer to [5, 11, 12]. We consider the p(x)-Laplacian equations with singular nonlinearities:. There are many results on the existence of positive solutions for p-Laplacian problems with singular nonlinearities (see [14,15,16,17,18]), but the results on the existence of positive solutions for p(x)-Laplacian problems with singular nonlinearities. Our results partially generalized the results of [18]
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