a note on existence of anti periodic and heteroclinic solutions for a class of second order odes abstract we discuss the existence of anti periodic solutions to the following second order differential equation q u t q by using fixed point theory together with the green s function for the anti periodic boundary value problem in the first part section 2 of the paper then in the next part section 3 we construct a kind of heteroclinic solution to some special cases of the equation above our method is variational in nature and is inspired by the ideas of rabinowitz and stredulinsky in p rabinowitz e stredulinsky on some results of moser and of bangert aihp anal nonlin 21 2004 673 688

guiding functions for generalized periodic problems and applications abstract in this paper developing the method of guiding functions for differential inclusions with a generalized periodic condition we obtain the existence theorem for such problems it is shown how the abstract result can be applied to the study of differential games and anti periodic problems

an efficient sequential quadratic programming algorithm for nonlinear programming in this paper a new feasible sequential quadratic programming fsqp algorithm is proposed to solve the nonlinear programming where a feasible descent direction is obtained by solving only one qp subproblem in order to avoid maratos effect a high order revised direction is computed by solving a linear system with involving some active constraints the theoretical analysis shows that global and superlinear convergence can be deduced

on a class of second order anti periodic boundary value problems of concern is the existence and uniqueness of anti periodic solutions to a class of abstract nonlinear second order differential equations the investigation relies on the theory of m accretive operators in banach or hilbert spaces examples of boundary value problems for ordinary and partial differential equations are also discussed

analysis and control of differential inclusions with anti periodic conditions we deal with the optimal control of systems driven by differential inclusions with anti periodic conditions in banach spaces the operators in the differential inclusions describing the control system all depend on control variables by a solution of the control system we mean a trajectory control pair we first prove that for fixed control variables the set of solutions is non empty for the corresponding differential inclusion with anti periodic conditions we then show the functional topological properties of the set of solutions finally we investigate the existence of solutions to the optimal control problem these abstract results can be used to study optimal control systems of evolutionary hemi variational inequalities

a quantization property for static ginzburg landau vortices for any critical point of the complex ginzburg landau functional in dimension 3 we prove that for large coupling constants if the energy of this critical point on a ball of a given radius r is relatively small compared to r log then the ball of half radius contains no vortex the modulus of the solution is larger than we then show how this property can be applied to describe limiting vortices as e 0 2001 john wiley sons inc

two results on the equivariant ginzburg landau vortex in arbitrary dimension we characterize the o n equivariant vortex solution for ginzburg landau type equations in the n dimensional euclidean space and we prove its local energy minimality for the corresponding energy functional

anti periodic solution forutt σ ux x uxxt f x t abstract existence of a smooth anti periodic solution for the quasilinear equationu tt sigma u x x u xxt f x t qquad hbox in 0 pi times bfr with the boundary conditionu 0 t u t 0 is proved for a class of v including sigma v v sqrt 1 v 2 wheref x t is a given anti periodic function int

existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities abstract in this paper we consider the problem of the existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities with a pseudomonotone operator using regularized approximating and first eigenfunction methods and the surjectivity result we prove the existence of solutions for quasilinear parabolic hemivariational inequalities

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

existence of anti periodic mild solutions for semilinear evolution equations in this paper we study the existence of anti periodic mild solutions for a class of semilinear evolution equations in banach spaces and extend some related results in this direction an example is given to illustrate our results

regularity of flat level sets in phase transitions we consider local minimizers of the ginzburg landau energy functional 1 2 u 2 1 4 1 u 2 2 dx and prove that if the 0 level set is included in a flat cylinder then in the interior it is included in a flatter cylinder as a consequence we prove a conjecture of de giorgi which states that level sets of global solutions of u u 3 u such that u 1 n u 0 lim u x x n 1 x n are hyperplanes in dimension n 8

asymptotics for the ginzburg landau equation in arbitrary dimensions let be a bounded simply connected regular domain of rn n 2 for 0 e 1 let ue c be a smooth solution of the ginzburg landau equation in with dirichlet boundary condition ge i e formula we are interested in the asymptotic behavior of ue as e goes to zero under the assumption that ee ue m0 log e and some conditions on ge which allow singularities of dimension n 3 on

anti periodic solutions to nonlinear evolution equations abstract we deal with anti periodic problems for nonlinear evolution equations with nonmonotone perturbations the main tools in our study are the maximal monotone property of the derivative operator with anti periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings

anti periodic oscillations of some second order differential equations and optimal control problems abstract this paper deals with periodic and anti periodic boundary conditions for wave and heat equations as well as for some second order ordinary differential equations optimal control problems associated with such equations are studied and some numerical experiments to determine the solution of the problem y t 3 sin t y t cos t 0 t y i 0 y i 0 i 0 1 are given some open problems related to the invertibility of i e ta are pointed out

closed range mild solution operators and nonconvex optimal control via orthogonality and generalized gradients let x be a banach space x its dual and h a hilbert space denote by the duality pairing i e x x x x and by the norm on both x and x for simplicity of writing the same notations will be used to denote the inner product and norm of both h and l2 0 t x consider the t periodic problem in x with t 0 y t a t y t f t a e t 0 t y 0 y t 1 1

anti periodic solutions to a class of nonlinear differential equations in hilbert space abstract a broad class of nonlinear non monotone anti periodic boundary value problems in a hilbert space is considered as a preliminary step the existence uniqueness and continuous dependence upon data of anti periodic solutions to some first and second order evolution equations associated to odd noncoercive monotone operators is established applications of the theory to nonlinear partial differential equations are also discussed

small energy ginzburg landau minimizers in r3 abstract we prove that a local minimizer of the ginzburg landau energy in r 3 satisfying the condition lim inf r e u b r r ln r 2 must be constant the main tool is a new sharp ellipticity result for minimizers in dimension three that might be of independent interest

entire solutions of semilinear elliptic equations in r 3 and a conjecture of de giorgi this paper is concerned with the study of bounded solutions of semilinear elliptic equations u f u in the whole space r under the assumption that u is monotone in one direction say nu in r n the goal is to establish the one dimensional character or symmetry of u namely that u only depends on one variable or equivalently that the level sets of u are hyperplanes this type of symmetry question was raised by de giorgi in who made the following conjecture we quote literally page of dg

periodic solutions of second order differential equations in banach spaces we use operator valued fourier multiplier theorems to study second order differential equations in banach spaces we establish maximal regularity results in l p and c s for strong solutions of a complete second order equation

nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators periodic problems where t is a given positive number a is the subdifferential of a timedependent lower semicontinuous convex function from h into 0 a with qf f co and where b t is a possibly nonmonotone multivalued nonlinear operator from d b t c h into h such that d c d b t m for all t e 0 t the case when b t is identically zero has been investigated by many authors see e g bknilan and b is 2 nagai 13 and yamada 20 as for the case when b t is not identically zero nor monotone however it seems that very little study has been devoted to this kind of problem on the other hand the cauchy problem for 1 1 has been studied by several authors i e attouch and damlamian 11 biroli 3 koi and watanabe 9 and the author 14 151 the main objective of the present paper is to pursue and develop the method employed in 151 for the periodic problem p p this paper is composed of five sections section 2 contains some preliminaries in section 3 we shall formulate main results in two distinctive types of theorems roughly speaking according to whether the external force f t can be taken arbitrarily large or not in section 4 we shall prove them by much the same method based on a schauder tychonoff type fixed point theorem as in 151 in section 5 it will be exemplified that our results give a 248 0022 0396184 3 00

a study on quasi periodic boundary value problems for nonlinear higher order impulsive differential equations a study concerning the solvability of the quasi periodic boundary value problems for nonlinear higher order impulsive differential equations is made sufficient conditions for the existence of at least one solution to the problems are obtained examples are presented to illustrate the main results

anti periodic solutions for semilinear evolution equations in this paper we use the homotopy method to establish the existence and uniqueness of anti periodic solutions for the nonlinear anti periodic problem a t x bx f t a e t r x t t x t where a t x is a nonlinear map and b is a bounded linear operator from r n to r n sufficient conditions for the existence of the solution set are presented also we consider the nonlinear evolution problems with a perturbation term which is multivalued we show that for this problem the solution set is nonempty and weakly compact in w 1 2 i r n for the case of convex valued perturbation and prove the existence theorems of anti periodic solutions for the nonconvex case all illustrative examples are provided

second order differential variational inequalities involving anti periodic boundary value conditions abstract this paper deals with a new class of second order nonlinear differential variational inequalities firstly we study the properties of a solution set for a variational inequality by using the kkm technique and a monotonicity property then we prove the existence of solutions to a second order nonlinear differential variational inequality with anti periodic boundary value conditions not assuming the lipschitz continuity of the nonlinear term our approaches which are essentially different from previous research methods in differential variational inequalities are based on the topological degree theory and the filippov implicit function lemma

existence of antiperiodic solutions for hemivariational inequalities in this paper we consider the problem of existence of antiperiodic solutions for first order and second order hemivariational inequalities with a pseudomonotone operator we first give the surjectivity result and then prove a existence of antiperiodic solutions for hemivariational inequalities with the surjectivity result

on de giorgi s conjecture in dimension n 9 a celebrated conjecture due to de giorgi states that any bounded solution of the equation u 1 u 2 u 0 in r n with ynu 0 must be such that its level setsfu g are all hyperplanes at least for dimension n 8 a counterexample for n 9 has long been believed to exist starting from a minimal graph which is not a hyperplane found by bombieri de giorgi and giusti in r n n 9 we prove that for any small 0 there is a bounded solution u y with yn u 0 which resembles tanh a t p 2 a where t t y denotes a choice of signed distance to the blown up minimal graph 1 this solution is a counterexample to de giorgi s conjecture for n 9