existence theorems for the one dimensional singular p laplacian equation with a nonlinear boundary condition in this paper general existence theorems are presented for the singular equation f p y q t f t y 0

a modified gpss method for non hermitian positive definite linear systems this paper is concerned with a modified version of the generalization of positive definite and skew hermitian splitting iteration mgpss to solve the non hermitian positive definite linear systems the theoretical analysis shows that the mgpss iteration method will converge unconditionally numerical examples are reported to confirm the efficiency of the proposed methods

a rational function preconditioner for indefinite sparse linear systems this paper introduces a rational function preconditioner for linear systems with indefinite sparse matrices a by resorting to rational functions of a the algorithm decomposes the spectrum of a into two disjoint regions and approximates the restriction of a 1 on these regions separately we show a systematic way to construct these rational functions so that they can be applied stably and inexpensively an attractive feature of the proposed approach is that the construction and application of the preconditioner can exploit two levels of parallelism moreover the proposed preconditioner can be modified at a negligible cost into a preconditioner for a nearby matrix of the form a ci which can be useful in some applications the efficiency and robustness of the proposed preconditioner are demonstrated on a few tests with challenging model problems including problems arising from the helmholtz equation in three dimensions

the becker doring equations at large times and their connection with the lsw theory of coarsening a systematic procedure is given for obtaining the asymptotic late time behavior of the becker doring equations describing the time evolution of a population of clusters of particles in lowest order of approximation the distribution of the sizes of the largest clusters satisfies the equations of the lifshitz slyozov wagner theory of coarsening

multiple positive solutions to singular boundary value problems for superlinear higher order odes for 1 k n 1 we study the existence of multiple positive solutions to the singular k n k conjugate boundary value problem 1 n ky n f t y 0 t 1 y i 0 0 0 i k 1 y i 0 0 0 i k 1 y j 1 0 0 j n k 1 we show that there are at least two positive solutions if f t y is is superlinear at and singular at u 0 t 0 and t 1 the arguments involve only positivity properties of green s function and a fixed point theorem in cones moreover the explicit formula of green s function can be found in this paper

a singular boundary value problem for the one dimensionalp laplacian abstract the singular boundary value problem formula is studied in this paper whereg s s p 2s p 1 the singularity may appear atu 0 and att 0 ort 1 and the functionfmay be discontinuous the authors prove that for anyp 1 and for any positive nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions the above mentioned problem has a unique solution also the properties of the solution are discussed in the paper

a block alternating splitting iteration method for a class of block two by two complex linear systems optimization problems with partial differential equations as constraints arise widely in many areas of science and engineering in this paper we focus on solving a class of block two by two complex linear systems arising from the distributed optimal control with time periodic parabolic equations a new block alternating splitting bas iteration method is presented for solving the class of complex linear systems the convergence theory and the spectral properties of the bas iteration method are discussed numerical experiments are presented to illustrate the efficiency of the bas iteration as a solver as well as a preconditioner for krylov subspace methods

solving shifted linear systems with restarted gmres augmented with error approximations abstract in this paper we investigate a variant of the restarted gmres method for solving a series of large sparse linear systems restarting is carried out by augmenting krylov subspaces with some recently generated error approximations from the seed system the method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix vector multiplication per iteration compared with solving each added linear system separately the advantage of the new scheme is to lower down the overall cost of solving all added linear systems numerical experiments illustrate the efficiency of the acceleration strategy

a singular nonlinear boundary value problem membrane response of a spherical cap the nonlinear boundary value problem y n x 2 32y 2 lambda 2 8 quad 0 0 nu 0 are constants models the large deflection membrane response of a spherical cap and has been solved numerically by various techniques in the engineering literature we prove existence and uniqueness of a solution of this problem provide qualitative information about the solution and use this information to suggest an approach to numerical computation

a parameterized shss iteration method for a class of complex symmetric system of linear equations in this paper we present a parameterized variant of the single step hermitian and skew hermitian shss iteration method for solving a class of complex symmetric system of linear equations we study the convergence properties of the parameterized shss p shss iteration method the choices of the parameters and the quasi optimal parameters numerical experiments are given to verify the effectiveness of the p shss iteration method

preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite linear systems for the positive semidefinite system of linear equations of a block two by two structure by making use of the hermitian skew hermitian splitting iteration technique we establish a class of preconditioned hermitian skew hermitian splitting iteration methods theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system moreover the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly numerical examples further confirm the correctness of the theory and the effectiveness of the method

a generalization of the hermitian and skew hermitian splitting iteration method for solving sylvester equations this paper is concerned with a generalization of the hermitian and skew hermitian splitting hss iteration method for solving large sparse continuous sylvester equations the analysis shows that the ghss iteration method will converge under certain assumptions numerical results show that this new method is more efficient and robust than the existing ones

efficient single step preconditioned hss iteration methods for complex symmetric linear systems abstract we propose a single step preconditioned variant of hss sphss and an efficient parameterized sphss psphss iteration method for solving a class of complex symmetric linear systems under suitable conditions we analyze the convergence properties of the sphss and psphss iteration methods theoretical analysis shows that the minimal upper bounds for the spectral radius of the sphss and psphss iteration matrices are less than those of the shss and pshss iteration matrices when using the optimal parameters respectively numerical results show that the psphss iteration method has comparable advantage over several other iteration methods whether the experimental optimal parameters are used or not

a new sor like method for the saddle point problems abstract in previous years golub wu and yuan presented a generalized successive over relaxation sor like method for solving the saddle point problems in this paper we present a new sor like nsor like method which has three parameters our new method can be applied to the nonsingular saddle point problems as well as the singular cases the characteristic of eigenvalues of the iteration matrix of this nsor like method is analyzed then we give the convergence semi convergence theorem of the new iterative method by giving the restrictions imposed on the parameter moreover that convergence semi convergence theorem is applied to some special cases to give the convergence region for the parameters we can see that nsor like method has a wider convergence semi convergence region for and than the parameterized uzawa method which covers preconditioned uzawa method and uzawa method in addition the optimal iteration parameters and the corresponding convergence semi convergence factor for the uzawa method are presented

twin solutions to singular dirichlet problems the existence of two nonnegative solutions to dirichlet second order boundary value problems is established in this paper our nonlinearity may be singular at y 0 t 0 and or t 1

positive solutions of singular p laplacian dynamic equations with sign changing nonlinearity abstract let t be a time scale such that 0 t t by the schauder fixed point theorem and the upper and lower solution method we present some existence criteria of the positive solution of m point singular p laplacian dynamic equation p u t q t f t u t 0 t 0 t t with boundary conditions u 0 0 i 1 m 1 i u i u t 0 m 2 where p s s p 2 s with p 1 i r r is continuous for i 1 2 m 1 and nonincreasing if m 3 0 1 2 m 2 m 1 t the nonlinear term may be singular in its dependent variable and is allowed to change sign our results are new even for the corresponding differential t r and difference equations t z as an application an example is given to illustrate our result

upper and lower solutions for the singular p laplacian with sign changing nonlinearities and nonlinear boundary data this paper presents existence results for singular p laplacian equations with nonlinear boundary data our nonlinearity f t u in the differential equation is allowed to change sign and the singularity may occur at u 0 t 0 and t 1

some remarks on large time asymptotic of the lifshitz slyozov equations we obtain an entropy functional for the lifshitz slyozov system this can be used to investigate the time asymptotics of the system in particular we describe situations in which the monomers concentration either tend to 0 or saturate as time becomes large the latter situation can be excluded under assumptions on the support of the initial data

triple positive solutions to third order three point bvp with increasing homeomorphism and positive homomorphism in this paper we investigate the existence of triple positive solutions for nonlinear differential equations boundary value problems with increasing homeomorphism and positive homomorphism operator by using fixed point theorems in cones we establish results on the existence of three positive solutions with suitable growth conditions imposed on the nonlinear term as applications two examples are given to demonstrate our result the conclusions in this paper essentially extend and improve the known results

a cocr method for solving complex symmetric linear systems the conjugate orthogonal conjugate gradient cocg method has been recognized as an attractive lanczos type krylov subspace method for solving complex symmetric linear systems however it sometimes shows irregular convergence behavior in practical applications in the present paper we propose a conjugate a orthogonal conjugate residual cocr method which can be regarded as an extension of the conjugate residual cr method numerical examples show that cocr often gives smoother convergence behavior than cocg

asymptotic behaviour of solutions to a simplified lifshitz slyozov equation abstract for the system c u 1 c u 0 c d 0 c d 1 we prove for several classes of initial data c 0 that lim 2 x c x d x h x where h is a known function determined by the behaviour of c 0 near the largest values in its support if c 0 has compact support near whose supremum a it behaves like a q q 1 then h also has compact support near whose supremum it behaves like a q 1 if c 0 goes to zero exponentially fast as a or if its support is infinite and it decays exponentially fast for large then h x is e x if c 0 has infinite support and decays for large like a negative power of then so does h we also give examples of initial data for which the above limit does not exist

on the fredholm alternative for the p laplacian in this paper we study the range of the operator u p 1 1 u p 2u email protected u p 2u email protected u p 2u u 0 u t 0 p 1 p p email protected psin p p a 0 b 0 and p 1 1 p a 1 p email protected 1 p 2 the results of this paper generalize the corresponding results obtained in j differential equations 151 1999 386 and the method used in this paper is elementary

existence theorems for the one dimensional singular p laplacian equation with sign changing nonlinearities in this paper general existence theorems are presented for the singular equation f p y f t y 0 y 0 y 1 0 throughout our nonlinearity is allowed to change sign

multiple positive solutions for the one dimensional singular p laplacian we consider the following boundary value problem f p y q t f y 0 p 1 t 0 1 with y 0 y 1 0 or y 0 y 1 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem an example is also included to illustrate the importance of the result obtained

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

multiple positive solutions for multipoint boundary value problems with sign changing nonlinearity abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u q t f t u 0 t 0 1 subject to the boundary value conditions u 0 i 1 n i u i u 1 i 1 n i u i where p s s p 2s p 1 i 0 1 with 0 1 2 n 1 and i i 0 satisfy 0 i 1 n i i 1 n i 1 the nonlinear term f may change sign using a fixed point theorem for operators in a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

non self similar behavior in the lsw theory of ostwald ripening the classical lifshitz slyozov wagner theory of domain coarsening predicts asymptotically self similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field here we consider the long time behavior of measure valued solutions for systems in which particle size is uniformly bounded i e for initial measures of compact support we prove that the long time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support we give a necessary criterion for convergence to other self similar solutions and conditional stability theorems for some such solutions for a dense set of initial data convergence to any self similar solution is impossible

upper and lower solutions method and a singular superlinear boundary value problem for the one dimensional p laplacian abstract the singular boundary value problem is studied in this paper where s s p 2 s p 1 the singularity may appear at u 0 t 0 and t 1 and the function g may be superlinear at u and change sign the existence of solutions is obtained via an upper and lower solutions method

on hermitian and skew hermitian splitting iteration methods for the linear matrix equation axb c in this paper a hermitian and skew hermitian splitting hss iteration method for solving the linear matrix equation axb c is proposed this method is formed by extending the corresponding hss iteration method for solving ax b the analysis shows that the hss iteration method will converge under certain assumptions moreover the optimal parameter of this iteration method is presented numerical results show that this new method is more efficient and robust than existing methods

multiple positive solutions to a class of singular boundary value problems for the one dimensional p laplacian abstract in this paper we establish the existence of multiple positive solutions to the singular nonlinear boundary value problem u q t f u t 0 0 1 the singularity may appear at u 0 and t 0

domain stability competition growth and selection in globally constrained bistable systems a general globally constrained reaction diffusion equation is suggested that describes formation of equilibrium domains and competition between domains in bistable media we study the stability properties of domains strips and perfect circlular or spherical drops in one two and three dimensions the dynamics of the distribution function df of many drops with respect to their radii is mapped into a mean field model of ostwald ripening a family of similarity solutions for the df is found and the long standing problem of selection rule for the correct asymptotic df is solved textcopyright 1996 the american physical society

on positive definite and skew hermitian splitting iteration methods for continuous sylvester equation ax xb c in this paper we present a positive definite and skew hermitian splitting pss iteration method for continuous sylvester equations ax xb c with positive definite semi definite matrices the theoretical analysis shows that the pss iteration method will converge unconditionally and the optimal parameter of the new method is presented moreover to reduce the computing cost an inexact variant of the pss iteration method ipss and the analysis of its convergence property in detail have been established numerical results show that this new method and its inexact invariant are efficient and robust solvers for this class of continuous sylvester equations

on existence of multiple positive solutions for ϕ laplacian multipoint boundary value abstract in this paper we consider the following multipoint boundary value problem with one dimensional laplacian x t q t f t x t x t 0 t 0 1 x 0 i 1 n 2 i x i x 1 i 1 n 2 i x i where is an odd and increasing homeomorphism i 0 1 with 0 1 2 n 2 1 i and i are nonnegative constants and f t x t x t is continuous and allowed to change sign by fixed point theorems we obtain new results on the existence of at least three positive solutions of this boundary value problem which includes and improves some related results in the relevant literature

positive solutions of nonlinear third order m point bvp for an increasing homeomorphism and homomorphism with sign changing nonlinearity in this paper several existence theorems of positive solutions are established for a nonlinear m point boundary value problem for the following third order differential equations f u a t f t u t 0 email protected 0 1 f u 0 email protected i 1m 2a email protected u x i u 0 0 u 1 email protected i 1m 2b iu x i where f email protected r is an increasing homeomorphism and homomorphism and f 0 0 the nonlinear term f may change sign as an application an example to demonstrate our results is given

existence theory for single and multiple solutions to singular positone boundary value problems abstract in this paper we present some old and new existence results for singular boundary value problems our nonlinearity may be singular in its dependent variable

efficient preconditioned nhss iteration methods for solving complex symmetric linear systems abstract based on the new hss nhss iteration method introduced by pour and goughery 2015 we propose a preconditioned variant of nhss p nhss and an efficient parameterized p nhss ppnhss iteration methods for solving a class of complex symmetric linear systems the convergence properties of the p nhss and the ppnhss iteration methods show that the iterative sequences are convergent to the unique solution of the linear system for any initial guess when the parameters are properly chosen moreover we discuss the quasi optimal parameters which minimize the upper bounds for the spectral radius of the iteration matrices numerical results show that the ppnhss iteration method is superior to several iteration methods whether the experimental optimal parameters are used or not

nonlinear superlinear singular and nonsingular second order boundary value problems abstract many new existence theorems are presented for singular and nonsingular second order boundary value problems singularities at y 0 t 0 and t 1 will be discussed

a single step iteration method for non hermitian positive definite linear systems abstract an efficient single step iteration method is presented for solving the large sparse non hermitian positive definite linear systems we theoretically prove that this method converges to the unique solution of the system of linear equations under suitable restrictions moreover we derive an upper bound for the spectral radius of the new iteration matrix furthermore we consider acceleration of the new iteration by krylov subspace methods and some special properties of the new preconditioned matrix are proposed numerical experiments on a few model problems are presented to further examine the effectiveness of our new method

upper and lower solutions and multiplicity results we consider the second order nonlinear differential equation with an unbounded right hand side and two point or nonlinear boundary conditions on a compact interval using the method of a priori estimates and the relation between the topological degree of the operators associated to the above boundary value problems and the strict lower and upper solutions we get the multiplicity results for the problems