the method of lower and upper solutions for 2nth order multi point boundary value problems abstract in this paper we consider the following 2 n th order multi point boundary value problems 1 n u 2 n t f t u t u t 1 i u 2 i t 1 n 1 u 2 n 2 t 0 t 1 with the 2 n m point boundary conditions u 2 j 0 u 2 j 1 0 j 0 1 2 m m n 2 u 2 j 0 a j u 2 j j 1 0 u 2 j 1 b j u 2 j j 2 0 j m 1 n 1 where a j 0 b j 0 0 j 1 j 2 1 j m 1 n 1 the existence of iterative solutions is obtained by using the lower and upper solution method for the above 2 n m point boundary value problems

absolutely γ summing multilinear operators abstract in this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators we show that several previous results on different contexts absolutely summability almost summability cohen summability are particular cases of our general results

multilinear variants of pietsch s composition theorem various concepts of multilinear summing operators were introduced in the last years by extending the well known one from the linear case in this paper we prove that as in the linear case there is a splitting theorem for dominated operators as a consequence of this result we prove various multilinear variants of pietsch s composition theorem

on the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions abstract we prove the existence of extremal solutions for the third order discontinuous functional nonlinear problem u t f t u u t u t for a e t a b u a a a r l 1 u u u a u b u a 0 l 2 u u a u b u b 0 by using a fixed point theorem after having established some existence results for some auxiliary second order nonlinear problems we observe that together with the discontinuities allowed on the spacial variable u with adequate modifications of technical type analogous results can be obtained when the equation has a second member not necessarily continuous in u

the method of lower and upper solutions for systems of boundary value problems the method of lower and upper solutions for second order differential system x f t x with dirichlet boundary condition x 0 x 1 0 is used to give sufficient conditions for the existence of at least one solution

hyper ideals of multilinear operators abstract we introduce and develop the notion of hyper ideals of multilinear operators between banach spaces while the well studied notion of ideals of multilinear operators multi ideals relies on the composition with linear operators the notion we propose by considering the composition with multilinear operators explores more deeply the nonlinear feature of the subject the results we prove show that although more restrictive a priori hyper ideals enjoy nice general properties and their theory is rich enough to provide distinguished examples in every situation where the corresponding multi ideal fails to be a hyper ideal

existence of solutions of boundary value problem for 3rd order nonlinear system by appropriate bounding function pair and modified functions using the theory of differential inequality and the theory of topological degree this paper presents the existence criterions of solutions for the system of 3rd order differential equations under nonlinear boundary conditions and extends many known results

bounding functions methods for fully nonlinear boundary value problems abstract using the bounding functions method and the theory of topological degree this paper presents the existence criterion of solution for third order bvp with nonlinear boundary conditions and extends the existing results

some techniques on nonlinear analysis and applications in this paper we present two different results in the context of nonlinear analysis the first one is essentially a nonlinear technique that in view of its strong generality may be useful in different practical problems the second result more technical but also connected to the first one is an extension of the well known pietsch domination theorem the last decade witnessed the birth of different families of pietsch domination type results and some attempts of unification our result that we call full general pietsch domination theorem is potentially a definitive pietsch domination theorem which unifies the previous versions and delimits what can be proved in this line the connections to the recent notion of weighted summability are traced

upper and lower solution methods for fully nonlinear boundary value problems abstract sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions the conditions assume the existence of a strong upper solution lower solution pair a concept that is defined in the paper the differential equation has nonlinear dependence on all lower order derivatives of the unknown in particular appropriate nagumo conditions are obtained and employed

kolmogorov equations in infinite dimensions well posedness and regularity of solutions with applications to stochastic generalized burgers equations we develop a new method to uniquely solve a large class of heat equations so called kolmogorov equations in infinitely many variables the equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper lyapunov type functions this way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly nonlocally lipschitz drifts apart from general analytic interest the main motivation is to apply this to uniquely solve martingale problems in the sense of stroock varadhan given by stochastic partial differential equations from hydrodynamics such as the stochastic navier stokes equations in this paper this is done in the case of the stochastic generalized burgers equation uniqueness is shown in the sense of markov flows

a generalized upper and lower solutions method and multiplicity results for nonlinear first order ordinary differential equations abstract we introduce a generalized upper and lower solutions method for the solvability of first order ordinary differential equations u t t u t u 0 u 1 in order to cover the case when the function satisfies caratheodory conditions this method is then applied to get multiplicity results when the nonlinearity interacts with the real eigenvalue of the linearized problem our proofs are based on differential inequalities and classical leray schauder degree

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

an abstract result on cohen strongly summing operators abstract we present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of cohen strongly summing linear operators our argument is extended to multilinear operators and as a consequence we establish some alternative characterizations for the class of cohen strongly summing multilinear operators

existence of solutions for a class of third order nonlinear boundary value problems abstract in this paper we are concerned with the following third order ordinary differential equation x t f t x t x t x t 0 0 with the nonlinear boundary conditions x 0 0 g x 0 x 0 a h x 1 x 1 b where a b r f 0 1 r 3 r is continuous g h r 2 r are continuous the existence result is given by using a priori estimate nagumo condition upper and lower solutions and leray schauder degree and we give an example to demonstrate our result

positive solutions of 2nth order ordinary differential equations with multi point boundary conditions in this paper we study the existence of positive solutions for 2nth order n 1 boundary value problems 1 nu 2n t f t u 0 t 1 subject to the 2 n m point boundary value conditions u 2j 0 u 2j 1 0 j 0 1 2 m m n 2 u 2j 0 bju 2j j 1 0 u 2j 1 dju 2j j 2 0 j m 1 n 1 where bj 0 dj 0 0 j 1 j 2 1 j m 1 n 1 by means of the fixed point theorems and the lower and upper solution method some results on the existence of positive solutions to the above 2 n m point boundary value problems are obtained

upper and lower solutions and topological degree this paper deals with second order nonlinear boundary value problems we suppose the existence of upper and lower solutions of the problems which are well ordered i e the lower solution is less than the upper one and we also consider the case of upper and lower solutions having the opposite ordering we prove the relation between the topological degree and strict upper and lower solutions in both cases and using this we get the existence and multiplicity results for the boundary value problems under consideration

summing multilinear operators by blocks the isotropic and anisotropic cases abstract unifying several directions of the development of the study of summing multilinear operators between banach spaces we construct a general framework that studies under one single definition multilinear operators that are summing with respect to sums taken over any number of indices iterated and non iterated sums the isotropic and the anisotropic cases sums over arbitrary blocks and over several different sequence norms a large number of special classes of multilinear operators and of methods of generating classes of multilinear operators are recovered as particular instances ideal properties and coincidence theorems for the general classes are proved

singularly perturbed third order boundary value problem for nonlinear systems abstract this paper deals with the existence of solutions to a singularly perturbed boundary value problem for third order nonlinear differential systems the authors construct an appropriate generalized lower solution upper solution pair a concept that is defined in this paper and employ the method of descent nagumo conditions algebraic boundary layer functions and volterra type integral operator to guarantee the existence of solutions of the problem the uniformly valid asymptotic estimate of the solutions is given as well the differential systems has nonlinear dependence on all over order derivatives of the unknown

upper and lower solutions for periodic problems upper and lower solutions method topological degree and miranda fixed point theorem are applied to obtain the existence of at least one periodic solution for second order and first order nonlinear differential systems

fourth order problems with fully nonlinear boundary conditions differential inequality method bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth order differential equations under nonlinear boundary conditions and many existing results are complemented

the two phase stochastic stefan problem this work is concerned with existence for a stochastic free boundary problem arising in phase transition the stefan two phase problem the existence of an invariant ergodic measure associated with the corresponding transition semigroup p t is also proved together with an integration by parts formula for the generator of p t

existence of multiple solutions for second order boundary value problems we give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y f x y y 0 x epsilon 0 1 y 0 0 y 1 in the special case f x y y f y greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions we give an example showing this latter result is sharp our results extend those of avery and of lakshmikantham et al

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when

upper and lower solutions for second order boundary value problems with nonlinear boundary conditions on demontre des theoremes d existence en utilisant des solutions superieures et inferieures