In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

Patterns in nature result from dynamic relationships of forces and constraints. What is analogous for patterns in art? Art is created by human hands motivated by inspiration and thought. It is the product of creativity and skill. Creativity is constrained by cognitive processes and skill by the limits of technology. Based upon the author’s studies of Oriental carpets, this paper suggests that p...

The unity of psychology as a science is to be found in its definition as the science of mental life, and its explanation of individual behavior in terms of mental states. This disciplinary focus will help negotiate psychology's relations with other disciplines, such as neuroscience and cognitive science. The unity within psychology between science and practice is to be found in a focus on scien...

Because of its structure and cultural, social and historical conditions, the country of Iran has various ethnic, religious, and racial types. On the other hand, as  an element of large Islamic nation, Iran encounters various complex cultural conditions. The nature and the origin of unity and unification are the common points between these organs at both national and Islamic nation's level. In f...

The TRUTH of our existence has not been detected by science so far. Why does theoretical physics know nothing about the essence of space, matter, energy and time? How can we come to the true knowledge about our existence? Let us look at the reason of critical situation in contemporary theoretical physics and show how critical logical thinking and reasoning can open the door to the truth. I am s...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.