M. B. Ghaemi - Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran G. A. Afrouzi - Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran S. H. Rasouli - Department of Mathematics, Faculty of Basic Sciences, Babol University of Technology, Babol, Iran M. Choubin - Department of Mathematics, Faculty of Basic Sciences, Payame Noor University, Tehran, Iran
In this paper, we prove the existence of positive weak solution for the nonlinear elliptic system \[ \begin{cases} -\Delta_p u=\lambda_1u^a+\mu_1v^b,\,\,\,\,\, x\in\Omega,\\ -\Delta_q v=\lambda_2u^c+\mu_2v^d,\,\,\,\,\, x\in\Omega,\\ u=0=v,\,\,\,\,\, x\in \partial \Omega. \end{cases} \] where \(\Delta_sz=div(|\nabla z|^{s-2}\nabla z), s>1, \lambda_1, \lambda_2, \mu_1\) and \(\mu_2\) are positive parameters, and \(\Omega\) is a bounded domain in \(R^N, a + c < p - 1\) and \(b + d < q - 1\). We also discuss a multiplicity result when \(0 < \lambda_1, \lambda_2, \mu_1, \mu_2<\lambda^* \) for some \(\lambda^* \). We obtain our results via the method of sub - and super solutions.
M. B. Ghaemi, G. A. Afrouzi, S. H. Rasouli, M. Choubin, On Critical Exponent for the Existence and Multiplicity of Positive Weak Solutions for a Class of (p, Q)-laplacian Nonlinear System, Journal of Mathematics and Computer Science, 3 (2011), no. 4, 432--439
Ghaemi M. B., Afrouzi G. A., Rasouli S. H., Choubin M., On Critical Exponent for the Existence and Multiplicity of Positive Weak Solutions for a Class of (p, Q)-laplacian Nonlinear System. J Math Comput SCI-JM. (2011); 3(4):432--439
Ghaemi, M. B., Afrouzi, G. A., Rasouli, S. H., Choubin, M.. "On Critical Exponent for the Existence and Multiplicity of Positive Weak Solutions for a Class of (p, Q)-laplacian Nonlinear System." Journal of Mathematics and Computer Science, 3, no. 4 (2011): 432--439
