positive soliton solutions for generalized quasilinear schrodinger equations with critical growth this paper is concerned with the positive solutions for generalized quasilinear schrodinger equations in rn with critical growth which have appeared from plasma physics as well as high power ultrashort laser in matter by using a change of variables and variational argument we obtain the existence of positive solutions for the given problem

soliton solutions for generalized quasilinear schrodinger equations abstract by introducing a new variable replacement we study the existence of nontrivial solutions for generalized quasilinear schrodinger equations which appear from plasma physics as well as high power ultrashort laser in matter

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

existence of a positive solution to kirchhoff type problems without compactness conditions abstract the existence of a positive solution to a kirchhoff type problem on r n is proved by using variational methods and the new result does not require usual compactness conditions a cut off functional is utilized to obtain the bounded palais smale sequences

soliton solutions for a class of quasilinear schrodinger equations with a parameter abstract combining variational methods with perturbation arguments we study the existence of nontrivial classical solution for the quasilinear schrodinger equation u v x u 2 u 2 u l u x r n where v r n r and l r r are continuous function is a parameter and n 3 this model has been proposed in plasma physics and nonlinear optics our main contribution is related to the fact that we are able to deal with the case 0

multiple solutions for a quasilinear schrodinger equation abstract in this paper we consider the quasilinear schrodinger equation u v x u u 2 u g x u x r n where g and v are periodic in x 1 x n and g is odd in u subcritical and satisfies a monotonicity condition we employ the approach developed in szulkin and weth 2009 2010 15 16 and obtain infinitely many geometrically distinct solutions

existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in rn abstract mountain pass in a suitable orlicz space is employed to prove the existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in r n these equations contain strongly singular nonlinearities which include derivatives of the second order such equations have been studied as models of several physical phenomena the nonlinearity here corresponds to the superfluid film equation in plasma physics

infinitely many radial solutions for kirchhoff type problems in rn abstract in this paper we concern with a class of kirchhoff type problems in r n by using the fountain theorem we obtain three existence results of infinitely many radial solutions for the problem

existence of ground state sign changing solutions for a class of generalized quasilinear schrodinger maxwell system in r3 abstract in this paper we study the existence of ground state sign changing solutions for the following generalized quasilinear schrodinger maxwell system d i v g 2 u u g u g u u 2 v x u g u g u k x f u x r 3 g 2 u x r 3 where g c 1 r r v x and k x are positive continuous functions and is a positive parameter by making a change of variable as u g 1 v and g u 0 u g t d t we obtain one ground state sign changing solution v g 1 u by using some new analytical skills and non nehari manifold method furthermore the energy of v g 1 u is strictly larger than twice that of the ground state solutions of nehari type we also establish the convergence property of v g 1 u as the parameter 0 our results improve and generalize some results obtained by chen and tang 2016 zhu et al 2016

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

existence and multiplicity of non trivial solutions for schrodinger kirchhoff type equations with radial potential abstract in the present paper the following schrodinger kirchhoff type problem p a b r n u 2 d x u v x u q x f u in r n u x 0 as x is studied four existence theorems of nontrivial solutions and a sequence of high energy solutions for problem p are obtained by the mountain pass theorem and symmetric mountain pass theorem

existence of solutions for a class of nonlinear schrodinger equations with potential vanishing at infinity abstract in this paper we investigate the existence of positive ground state solution for the following class of elliptic equations u v x u k x f u in r n where n 3 v k are nonnegative continuous functions and f is a continuous function with a quasicritical growth here we prove a hardy type inequality and use it together with variational method to get a ground state solution

bandwidth consecutive multicolorings of graphs abstract let g be a simple graph in which each vertex v has a positive integer weight b v and each edge v w has a nonnegative integer weight b v w a bandwidth consecutive multicoloring of g assigns each vertex v a specified number b v of consecutive positive integers so that for each edge v w all integers assigned to vertex v differ from all integers assigned to vertex w by more than b v w the maximum integer assigned to a vertex is called the span of the coloring in the paper we first investigate fundamental properties of such a coloring we then obtain a pseudo polynomial time exact algorithm and a fully polynomial time approximation scheme for the problem of finding such a coloring of a given series parallel graph with the minimum span we finally extend the results to the case where a given graph g is a partial k tree that is g has a bounded tree width

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

multiple solutions to a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation abstract in this paper we consider a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation under the assumption that the potential may be vanishing at infinity the existence of both the ground state and the ground state sign changing solutions is established furthermore the behavior of these solutions is studied when the perturbation vanishes it is a surprise that we find an interesting phenomenon about the monotonicity for the quotient function as a byproduct

existence of solutions for a quasilinear schrodinger equation with subcritical nonlinearities abstract in this paper we consider the existence of solutions for the quasilinear schrodinger equation u v x u u 2 u g x u in r n where n 3 and g x u is a superlinear but subcritical function under periodic or asymptotically periodic assumptions on the nonlinearities we prove the existence of bounded states for this equation by the mountain pass theorem

sign changing solutions for a class of kirchhoff type problem in bounded domains abstract we are interested in the existence of least energy sign changing solutions for a class of kirchhoff type problem in bounded domains because the so called nonlocal term b u 2 d x u is involving in the equation the variational functional of the equation has totally different properties from the case of b 0 combining constraint variational method and quantitative deformation lemma we prove that the problem possesses one least energy sign changing solution u b moreover we show that the energy of u b is strictly larger than the ground state energy finally we regard b as a parameter and give a convergence property of u b as b 0

nodal soliton solutions for quasilinear schrodinger equations with critical exponent this paper is concerned with constructing nodal radial solutions for quasilinear schrodinger equations in rn with critical growth which have appeared as several models in mathematical physics for any given integer k 0 by using a change of variables and minimization argument we obtain a sign changing minimizer with k nodes of a minimization problem since the critical exponent appears and the lower order term may change sign we should use more delicate arguments

multiple solutions for quasilinear schrodinger equations with a parameter abstract in this paper we study the following quasilinear schrodinger equations of the form u v x u u 2 u 2 2 u g x u x r n where 1 1 2 v c r n r g c r n r r using some special techniques the existence of positive solutions negative solutions and sequence of high energy solutions are studied

global existence of small solutions to a relativistic nonlinear schrodinger equation on etudie le probleme de cauchy associea une equation de schrodinger non lineaire modelisant une impulsion laser ultra intense et ultra courte dans un plasma les termes non lineaires nouveaux sont dus aux effets relativistes et a la force ponderomotrice nous prouvons l existence locale et l unicite de solutions petites lorsque la dimension de l espace transverse est egale a 2 ou 3 ainsi que l existence locale pour des donnees initiales de taille arbitraire en dimension un d espace transverse

sign changing and multiple solutions of kirchhoff type problems without the p s condition abstract the existence of nontrivial solutions of kirchhoff type equations is an important nonlocal quasilinear problem in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4 superlinear kirchhoff type problems without the p s condition one concerning the existence of a nontrivial solution and the other one concerning the existence of sign changing solutions and multiple solutions a b u 2 u f x u in u 0 on

sign changing solutions of kirchhoff type problems via invariant sets of descent flow we obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow

efficient approximation algorithms for bandwidth consecutive multicolorings of graphs let g be a graph in which each vertex v has a positive integer weight b v and each edge v w has a nonnegative integer weight b v w a bandwidth consecutive multicoloring simply called a b coloring of g assigns each vertex v a specified number b v of consecutive positive integers as colors of v so that for each edge v w all integers assigned to vertex v differ from all integers assigned to vertex w by more than b v w the maximum integer assigned to vertices is called the span of the coloring the b coloring problem asks to find a b coloring of a given graph g with the minimum span in the paper we present four efficient approximation algorithms for the problem which have theoretical performance guarantees for the computation time the span of a found b coloring and the approximation ratio we also obtain several upper bounds on the minimum span expressed in terms of the maximum b degrees one of which is an extension of brooks theorem on an ordinary coloring

addendum minimum weighted coloring of triangulated graphs with application to maximum weight vertex packing and clique finding in arbitrary graphs efficient algorithms are known for finding a maximum weight stable set a minimum weighted clique covering and a maximum weight clique of a vertex weighted triangulated graph however there is no comparably efficient algorithm in the literature for finding a minimum weighted vertex coloring of such a graph this paper gives an o v 2 procedure for the problem algorithm 1 it then extends the procedure to the problem of finding in an arbitrary graph g v e a maximal induced subgraph g w color equivalent as defined in 3 to a maximal triangulated subgraph g t algorithm 2 finally it uses this latter algorithm as the main ingredient of a branch and bound procedure for the maximum weight clique problem in an arbitrary graph computational experience is presented on arbitrary random graphs with up to 2 000 vertices

uniqueness of the ground state solutions of quasilinear schrodinger equations abstract we are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics we convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity we also investigate the non degeneracy of a positive radial solution for a converted semilinear elliptic equation

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

existence and multiplicity of solutions for kirchhoff type equations abstract in this paper the existence and multiplicity of weak solutions are obtained for a class of kirchhoff type problems with dirichlet boundary value conditions by using the mountain pass theorem the local linking theorem the fountain theorem and the symmetric mountain pass lemma in critical point theory

an evolutionary approach for bandwidth multicoloring problems in this paper we consider some generalizations of the vertex coloring problem where distance constraints are imposed between adjacent vertices bandwidth coloring problem and each vertex has to be colored with more than one color bandwidth multicoloring problem we propose an evolutionary metaheuristic approach for the first problem combining an effective tabu search algorithm with population management procedures the approach can be applied to the second problem as well after a simple transformation computational results on instances from the literature show that the overall algorithm is able to produce high quality solutions in a reasonable amount of time outperforming the most effective algorithms proposed for the bandwidth coloring problem and improving the best known solution of many instances of the bandwidth multicoloring problem