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

multiplicity of stationary solutions to the euler poisson equations abstract consider the system of euler poisson as a model for the time evolution of gaseous stars through the self induced gravitational force we study the existence uniqueness and multiplicity of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy a priori these results generalize the previous works on the irrotational or the rotational gaseous stars around an axis and then they hold in more general physical settings under the assumption of radial symmetry the monotonicity properties of the radius of the gas with respect to either the strength of the velocity field or the center density are also given which yield the uniqueness under some circumstances

uniqueness and nonuniqueness for positive radial solutions of δu f u r 0 on considere le probleme de l unicite pour les solutions positives du probleme de dirichlet non lineaire u f u x 0 dans u 0 est une boule ou un anneau de r n et f 0 est superlineaire en u et satisfaisait f 0 x 0

uniqueness of positive solutions of a quasilinear dirichlet problem with exponential nonlinearity uniqueness of positive solutions of the following equation has been obtained where b n is the ball of unit radius and 0 moreover if n 2 then the solutions are nondegenerate

positive radial solutions for quasilinear systems in an annulus abstract we show that either superlinearity or sublinearity assumptions can guarantee the existence of positive radial solutions for quasilinear systems involving the p laplacian

weighted sobolev spaces with applications to singular nonlinear boundary value problems abstract variational methods are used in a weighted sobolev space to prove the existence of solutions for a certain class of singular nonlinear ordinary differential equations

uniqueness theorems for negative radial solutions of k hessian equations in a ball abstract in this paper we apply a pohozaev type identity and the monotone separation techniques to prove the uniqueness of negative radial solutions of k hessian equations in a finite ball

uniqueness of positive radial solutions for δu u up 0 on an annulus abstract we prove uniqueness of positive radial solutions to the semilinear elliptic equation u u u p 0 p 1 subject to the dirichlet boundary condition on an annulus in r n n 3 as a by product our argument also provides a much simpler if not the simplest new proof for the uniqueness of positive solutions to the same problem in a finite ball or in the whole space r n

existence result for impulsive third order periodic boundary value problems this paper is devoted to the study of periodic boundary value problems for nonlinear third order differential equations subjected to impulsive effects we provide sufficient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one periodic solution our approach is based on a priori estimates the method of upper and lower solutions combined with an iterative technique which need not be monotone

existence of positive nonradial solutions for nonlinear elliptic equations in annular domains we study the existence of positive nonradial solutions of equation a f u 0 in sia u 0 on d la where s x 6 w a 2 and is positive and superlinear at both 0 and oo we use a bifurcation method to show that there is a nonradial bifurcation with mode k at ak 0 1 for any positive integer k if is subcritical and for large k if is supercritical when is subcritical then a nehari type variational method can be used to prove that there exists a e 0 1 such that for any a e a 1 the equation has a nonradial solution on 0 a

uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations in this article we are concerned with the semilinear elliptic equation where n 2 p 1 and k lxl 0 in r n the correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived in addition we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on k and p furthermore based on the pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions we obtain the whole structure of radial solutions depending on various situations

comparison theorems for radial solutions of semilinear elliptic equations on obtient des resultats sur les solutions radiales des equations elliptiques de la forme u f u 0

infinitely many non radial solutions to a critical equation on annulus abstract in this paper we build infinitely many non radial sign changing solutions to the critical problem p u u 4 n 2 u in u 0 on on the annulus x r n a x b n 3 in particular for any integer k large enough we build a non radial solution which look like the unique positive solution u 0 to p crowned by k negative bubbles arranged on a regular polygon with radius r 0 such that r 0 n 2 2 u 0 r 0 max a r b r n 2 2 u 0 r

positive solutions to singular and non singular second order boundary value problems abstract the existence of positive solutions to second order singular boundary value problems is established our analysis is based on the topological transversality theorem of andrzej granas which relies on the notions of an essential map and a priori estimates on solutions

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

c i positive solutions of nonlinear singular differential equations for nonmonotonic function terms abstract suppose f t u v is nonnegative continuous on 0 1 r r and nondecreasing on u and nonincreasing on v for each fixed t there exist real numbers a 0 1 b 0 such that for any 0 r 1 f t r u v r a f t u v f t u r v r b f t u v u v r r then a necessary and sufficient condition for the boundary value problem u f t u u 0 0 t 1 u 0 u 0 0 u 1 u 1 0 to have c 0 1 positive solutions is that 0 0 1 g s s f s 1 1 d s where r 0 are nonnegative real numbers 0 and g t s is green s function of the above problem when f x u u 0

exact multiplicity and numerical computation of solutions for two classes of non autonomous problems with concave convex nonlinearities abstract we establish the exact multiplicity of positive solutions and the global solution structure for two classes of problems on circular domains the first class involves non autonomous concave convex problems on a ball in r n and the second one deals with concave convex problems on a thin annulus in r n we illustrate our results by numerical computations using a novel algorithm which involves continuation in a global parameter

on linearity of finitely generated r analytic groups in this paper we prove that if r is a commutative noetherian local pro p domain of characteristic 0 then every finitely generated r standard group is linear

nonlinear third order differential equations with anti periodic boundary conditions and some optimal control problems abstract existence uniqueness and continuous dependence theorems for a class of third order differential equations with anti periodic boundary conditions are given applications to optimal control of the deflection of a three layer beam are also given the methods used here are the leray schauder s continuation theorem the wirtinger poincare type inequalities the monotonicity method maximal monotone operators and the penalizations of convex functionals of barbu s type

a uniqueness result for a semilinear elliptic problem a computer assisted proof abstract starting with the famous article a gidas w m ni l nirenberg symmetry and related properties via the maximum principle comm math phys 68 1979 209 243 many papers have been devoted to the uniqueness question for positive solutions of u u u p in u 0 on where p 1 and ranges between 0 and the first dirichlet eigenvalue 1 of for the case when is a ball uniqueness could be proved mainly by ode techniques but very little is known when is not a ball and then only for 0 in this article we prove uniqueness for all 0 1 in the case 0 1 2 and p 2 this constitutes the first positive answer to the uniqueness question in a domain different from a ball our proof makes heavy use of computer assistance we compute a branch of approximate solutions and prove existence of a true solution branch close to it using fixed point techniques by eigenvalue enclosure methods and an additional analytical argument for close to 1 we deduce the non degeneracy of all solutions along this branch whence uniqueness follows from the known bifurcation structure of the problem

new exact multiplicity results with an application to a population model we obtain some new exact multiplicity results for the dirichlet boundary value problem on a unit ball b n in r n we consider several classes of nonlinearities f u including both positive and sign changing cases a crucial part of the proof is to establish positivity of solutions for the corresponding linearized problem as an application we obtain exact multiplicity results for the holling tanner population model

existence results of steady states of semilinear reaction diffusion equations and their applications partially supported by the applied mathematical sciences subprogram of the offlice of energy research u s department of energy under contract w 31 109 eng 38 while a visit ing scientist at argonne national laboratory during the summer of 1987 and m part by the board of regents of the state of louisiana under grant leqsf 86 89 rd a 11 partially supported by the applied mathematical sciences subprogram of the office of energy research u s department of energy under contract w 31 109 eng 38 this author thanks the department of mathematics university of southwestern louisiana for an invitation to spend a semester there in the fall of 1986 during which the research reported in this paper was started

solutions of euler poisson equations for gaseous stars in this paper we study the euler poisson equations governing gas motion under self gravitational force we are interested in the evolution of the gaseous stars for which the density function has compact support we establish existence theory for the stationary solutions and describe the behavior of the solutions near the vacuum boundary the boundary behavior thus obtained agrees with the physical boundary condition proposed and studied in l ly for both euler equations with damping and the euler poisson equations existence non existence uniqueness and instability of the stationary solutions with vacuum are also discussed in terms of the adiabatic exponent and the entropy function and the phenomena of the blowup that is the collapsing of the star to a single point with finite mass as well as the drifting of part of the star to infinity in space are also studied and shown to agree with the conjecture from the physical considerations

existence of solutions for anti periodic boundary value problems abstract by using schauder s fixed point theorem and the lower and upper solutions method we discuss the anti periodic boundary value problem for a class of second order differential equations some sufficient conditions for the existence of solutions are obtained

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

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

some superlinear problems with nonlocal diffusion coefficient abstract we study a superlinear elliptic problem with a non local diffusion coefficient we show that there exists a drastic change on the structure of the set of positive solutions when the non local coefficient grows fast enough to infinity we combine mainly sub super and bifurcation methods to obtain our results

nontrivial solutions for the equations of monge ampere type on etudie les solutions strictement convexes des equations de type monge ampere detu xd i xd j u p dans la boule b x 0 p n est un parametre reel on demontre l existence et l unicite

proof of a conjecture for the perturbed gelfand equation from combustion theory abstract in this paper we prove that when the domain b is a two dimensional ball for all small positive e the solution curve u of the perturbed gelfand equation u eu 1 eu with u b 0 is exactly s shaped this settles a long standing conjecture on the exact number of solutions to this equation