Search

A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.

In this article a nonlocal elliptic problem involving $p$-Laplacian on unbounded domain is considered. Using variational methods and under suitable conditions, the existence of a sequence of radially symmetric weak solutions, in two different cases, is proved.

In this paper, by applying the theory of condensing multimaps and the topological degree, wedeal with the existence of solutions for boundary value problems with second order differential inclusionsin different cases where the underlying space is a Banach space. Indeed, we investigate the existence ofsolutions for the BVP(x′′(t) ∈ F(t, x(t)) t ∈ I = [0,1],x(0) = x(1) = 0,where X is a real Banach space and the multifunction F : I ×X ⊸ K(X), in one case, has convex values andin another case has non-convex values (K(X) denotes compact subsets of X). Moreover, some results on theexistence of solutions for the extended version of BVP(u′′(t) ∈ Q(u) t ∈ I,u(0) = u(1) = 0,are presented, where Q :C(I,X) ⊸C(L 2) is a multimap satisfying some appropriate conditions. Finally, weshow how the results can be used to study periodic feedback control systems

In this paper, the existence of a fixed point for TF -contractive mappings on complete metric spaces and cone metric spaces is proved, where T : X → X is a one to one and closed graph function and F : P → P is non-decreasing and right continuous, with F -1(0) = -0} and F(tn ) → 0 implies tn → 0. Our results, extend previous results given by Meir and Keeler (J. Math. Anal. Appl. 28, 326-329, 1969), Branciari (Int. J. Math. sci. 29, 531-536, 2002), Suzuki (J. Math. Math. Sci. 2007), Rezapour et al. (J. Math. Anal. Appl. 345, 719-724, 2010), Moradi et al. (Iran. J. Math. Sci. Inf. 5, 25-32, 2010) and Khojasteh et al. (Fixed Point Theory Appl. 2010). MSC(2000): 47H10; 54H25; 28B05.