Periodic solutions for second order differential inclusions with the scalar p-Laplacian

We study periodic problems driven by the scalar p-Laplacian with a multivalued right-hand side nonlinearity. We prove two existence theorems. In the first, we assume nonuniform nonresonance conditions between two successive eigenvalues of the negative p-Laplacian with periodic boundary conditions. In the second, we employ certain Landesman-Lazer type conditions. Our approach is based on degree theory.     

Existence of positive solutions for the p-Laplacian with p-gradient term

In this paper, we study the existence of positive solutions for the p-Laplacian involving a p-gradient term. Due to the non-variational structure and the fact that the nonlinearity may be critical or supercritical, the variational method is no longer valid. Taking advantage of global C1,α estimates and the Liouville type theorems, we employ the blow-up argument to obtain the a priori estimates on solutions, and finally obtain the existence result based on the Krasnoselskii fixed point theorem.     

KKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces

A new KKM type theorem is first proved under noncompact setting of FC-spaces. As applications of the KKM type theorem, we establish some new existence theorems of solutions for generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

Absolute optimal solution for a compact and convex game

This paper investigates the existence of absolute optimal solutions for a partition P in continuous and quasiconcave games. We show that the P-consistency property introduced in the paper, together with the quasiconcavity and continuity of payoffs, permits the existence of P-absolute optimal solutions in games with compact and convex strategy spaces. The P-consistency property is a general condition that cannot be dispensed with for the existence of P-absolute optimal solutions. We also characterize the existence of P-absolute optimal solutions by providing necessary and sufficient conditions. Moreover, we suggest an algorithm for efficiently computing P-absolute optimal solutions.     

Multiple positive solutions of singular eigenvalue type problems involving the one-dimensional p-Laplacian

We establish a existence result of multiple positive solutions for a singular eigenvalue type problem involving the one-dimensional p-Laplacian. Furthermore, we obtain a nonexistence result of positive solutions by taking advantage of the internal geometric properties related to the problem. Our approach is based on the fixed point index theory and the fixed point theorem in cones.     

The homogeneous dirichlet problem for quasilinear anisotropic degenerate parabolic-hyperbolic equation with L initial value

The aim of this paper is to prove the well-posedness (existence and uniqueness) of the L^p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L^p initial value. We use the device of doubling variables and some technical analysis to prove the uniqueness result. Moreover we can prove that the L^p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.     

The Liouville-Bratu-Gelfand Problem for Radial Operators

We determine precise existence and multiplicity results for radial solutions of the Liouville-Bratu-Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.     

Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems

This paper deals with the existence of symmetric positive solutions for a class of singular Sturm-Liouville-like boundary value problems with a one-dimensional p-Laplacian operator. By using the fixed theorem of cone expansion and compression of norm type in a cone, the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function.     

Multiple positive solutions of the one-dimensional p-Laplacian

In this work we investigate the existence of positive solutions of the p-Laplacian, using the quadrature method. We prove the existence of multiple solutions of the one-dimensional p-Laplacian for α?0, and determine their exact number for α=0.     

Collective fixed points and maximal elements with applications to abstract economies

In this paper, we first establish collective fixed points theorems for a family of multivalued maps with or without assuming that the product of these multivalued maps is Φ-condensing. As an application of our collective fixed points theorem, we derive the coincidence theorem for two families of multivalued maps defined on product spaces. Then we give some existence results for maximal elements for a family of L_S-majorized multivalued maps whose product is Φ-condensing. We also prove some existence results for maximal elements for a family of multivalued maps which are not L_S-majorized but their product is Φ-condensing. As applications of our results, some existence results for equilibria of abstract economies are also derived. The results of this paper are more general than those given in the literature.     

Existence of periodic solutions for neutral type cellular neural networks with delays

In this paper, by using the theory of abstract continuation theorem of k contractive operator, we study the existence of periodic solutions for neutral type cellular neural networks with delays.     

The Leray-Schauder condition for 1-set weakly-contractive and (ws)-compact operators

The main purpose of this article is to prove a collection of new fixed point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray-Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for (ws)-compact (in particular nonexpansive) self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.     

Coefficient bounds for biholomorphic mappings which have a parametric representation

The main purpose of this paper is to prove a collection of new fixed point theorems for so-called weakly F-contractive mappings. By analogy, we introduce also a class of strongly F-expansive mappings and we prove fixed point theorems for such mappings. We provide a few examples, which illustrate these results and, as an application, we prove an existence and uniqueness theorem for the generalized Fredholm integral equation of the second kind. Finally, in Appendix A, we apply the Mönch fixed point theorem to prove two results on the existence of approximate fixed points of some continuous mappings.     

A class of semigroups regularized in space and time

We consider α-times integrated C-regularized semigroups, which are a hybrid between semigroups regularized in space (C-semigroups) and integrated semigroups regularized in time. We study the basic properties of these objects, also in absence of exponential boundedness. We discuss their generators and establish an equivalence theorem between existence of integrated regularized semigroups and well-posedness of certain Cauchy problems. We investigate the effect of smoothing regularized semigroups by fractional integration.     

Existence and multiplicity results for Dirichlet problems with p-Laplacian

In this paper we apply Morse theory to study the existence of nontrivial solutions of p-Laplacian type Dirichlet boundary value problems.     

On low degree k-ordered graphs

A simple graph G is k-ordered (respectively, k-ordered hamiltonian) if, for any sequence of k distinct vertices v₁,…,v_k of G, there exists a cycle (respectively, a hamiltonian cycle) in G containing these k vertices in the specified order. In 1997 Ng and Schultz introduced these concepts of cycle orderability, and motivated by the fact that k-orderedness of a graph implies (k-1)-connectivity, they posed the question of the existence of low degree k-ordered hamiltonian graphs. We construct an infinite family of graphs, which we call bracelet graphs, that are (k-1)-regular and are k-ordered hamiltonian for odd k. This result provides the best possible answer to the question of the existence of low degree k-ordered hamiltonian graphs for odd k. We further show that for even k, there exist no k-ordered bracelet graphs with minimum degree k-1 and maximum degree less than k+2, and we exhibit an infinite family of bracelet graphs with minimum degree k-1 and maximum degree k+2 that are k-ordered for even k. A concept related to k-orderedness, namely that of k-edge-orderedness, is likewise strongly related to connectivity properties. We study this relation and give bounds on the connectivity necessary to imply k-(edge-)orderedness properties.     

A priori estimates and existence of positive solutions for strongly nonlinear problems

In this paper we study the existence of positive solutions for a nonlinear Dirichlet problem involving the m-Laplacian. The nonlinearity considered depends on the first derivatives; in such case, variational methods cannot be applied. So, we make use of topological methods to prove the existence of solutions. We combine a blow-up argument and a Liouville-type theorem to obtain a priori estimates. Some Harnack-type inequalities which are needed in our reasonings are also proved.     

A system of coupled pendulii

We study the existence of solutions for a coupled system of n-dimensional pendulum equations under generalized periodic-type conditions. We obtain existence results under appropriate conditions using topological degree methods and a shooting type argument.     

Infinitely many radial solutions for a p-Laplacian problem p-superlinear at the origin

We prove the existence of infinitely many radial solutions for a p-Laplacian Dirichlet problem which is p-superlinear at the origin. The main tool that we use is the shooting method. We extend for more general nonlinearities the results of J. Iaia in [J. Iaia, Radial solutions to a p-Laplacian Dirichlet problem, Appl. Anal. 58 (1995) 335-350]. Previous developments require a behavior of the nonlinearity at zero and infinity, while our main result only needs a condition of the nonlinearity at zero.     

T- and Hayman T-points of meromorphic functions for small functions in the unit disk

In this article, we consider the singular points of meromorphic functions in the unit disk. We prove the second fundamental theorem for the Ahlfors-Shimizu's characteristic in the unit disk in terms of Nevanlinna theory in the angular domains, and obtain the existence of T-points and Hayman T-points dealing with small functions as target.