positive radial solutions and non radial bifurcation for semilinear elliptic equations in annular domains abstract we discuss the existence and multiplicity of positive radial solutions and the non radial bifurcation of u f u 0 in and u 0 on where is an annular domain of r n n 2 we prove that if f u 0 for u 0 and lim u f u u then there exists 0 such that there are at least two positive radial solutions for each 0 at least one for and none for if f 0 0 lim u 0 f u u 1 and uf u 1 e f u for u 0 e 0 then there exists a variational solution for 0 1 where 1 is the least eigenvalue of if f 0 0 lim u 0 f u u 0 and lim u f u u then there exists at least one positive radial solution for any 0 we obtain some precise multiplicity results for narrow annulus and show that the non radial bifurcation occurs if the growth of f u is rapid enough as u

a complete classification of bifurcation diagrams of a dirichlet problem with concave convex nonlinearities abstract we study the bifurcation diagrams of positive solutions of the two point boundary value problem u x f u x 0 1 u 1 u 1 0 where f u g u h u g h c 0 c2 0 and 0 is a bifurcation parameter we assume that functions g and h satisfy hypotheses h1 h3 under hypotheses h1 h3 we give a complete classification of bifurcation diagrams and we prove that on the u plane each bifurcation diagram consists of exactly one curve which is either a monotone curve or has exactly one turning point where the curve turns to the left hence the problem has at most two positive solutions for each 0 more precisely we prove the exact multiplicity of positive solutions

uniqueness results for the one dimensional p laplacian this paper is concerned with positive solutions of the boundary value problem y p 2y f y 0 y b 0 y b where p 1 b is a positive parameter assume that f is continuous on 0 changes sign from nonpositive to positive and f y yp 1 is nondecreasing in the interval of f 0 the uniqueness results are proved using a time mapping analysis

natural coordinate system approach to coupled n phase fluid flow in curved domains a natural coordinate system is introduced in this work to handle the flow of a multiphase fluid in domains possessing curved boundaries a multiple transformation that is capable of mapping a single physical domain onto a single computational domain is derived this work furnishes the necessary theoretical foundation for the concept of natural coordinate systems for multiphase flows

emden fowler equations involving critical exponents on considere le probleme y t k y 2 y 2k 3 0 t 0 pour t 2 0 0 soit t inf t 0 y 0 sur t alors t 0 0 on etudie comment la position t du premier zero de y t varie avec

hilbert s projective metric and nonlinear elliptic problems abstract this paper deals with the eigenvalue problems for a class of positive nonlinear operators the projective metric technique is used to prove the existence of a unique fixed point of the operator we then show how to apply our results to the study of nonlinear elliptic problems

existence of positive solutions for non positive higher order bvps abstract we shall provide conditions on non positive function f t u 1 u n 1 so that the boundary value problem has at least one positive solution then we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions

uniqueness of positive radial solutions for semilinear elliptic equations on annular domains where 5 5a b x rn 0iai x ib is an annular domain in rn n 3 it is well known that the uniqueness problems of solutions of 1 1 and 1 2 are both fundamental and often di8cult during the last decade there has been tremendous progress in studying these problems when 5 is a ball in rn or entire rn n 3 see e g 1 2 5 10 11 however very little was known concerning the annular domain until the work of ni and nussbaum 12 until very recently co man 3 showed that when n 3 f u u up 1ip 3 1 1 and 1 2 have unique positive radial solution for any annular domain see also 13 then it is of interest to extend co man s result to a more general situation for example we may ask the following question

positive solutions of difference equations with two point right focal boundary conditions abstract we consider the following boundary value problem formula formula where 1 p n 1 is fixed using a fixed point theorem for operators on a cone we develop criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are established for special cases we also include several examples to dwell upon the importance of the results obtained

asymptotic behavior of positive solution in an annulus abstract this paper concerns the positive solutions of superlinear elliptic equation with hardy potential u x 2 u u p 2 u in u 0 in u 0 on where is an annulus of r n n 2 we obtain qualitative properties of solutions as p

on uniqueness for nonlinear elliptic equation involving the pucci s extremal operator abstract in this article we study uniqueness of positive solutions for the nonlinear uniformly elliptic equation m d 2 u u u p 0 in r n lim r u r 0 where m d 2 u denotes the pucci s extremal operator with parameters 0 and p 1 it is known that all positive solutions of this equation are radially symmetric with respect to a point in r n so the problem reduces to the study of a radial version of this equation however this is still a nontrivial question even in the case of the laplacian the pucci s operator is a prototype of a nonlinear operator in no divergence form this feature makes the uniqueness question specially challenging since two standard tools like pohozaev identity and global integration by parts are no longer available the corresponding equation involving m is also considered

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

separation of branches of o n 1 invariant solutions for a semilinear elliptic equation abstract we consider the problem u u u p in a u 0 in a u 0 on a where a is an annulus in r n n 2 p 1 and 0 recent results ensure that there exists a sequence p k of exponents p k at which a nonradial bifurcation from the radial solution occurs exploiting the properties of o n 1 invariant spherical harmonics we introduce two suitable cones k 1 and k 2 of o n 1 invariant functions that allow to separate the branches of bifurcating solutions getting their unboundedness

exact multiplicity for degenerate two point boundary value problems with p convex nonlinearity the exact number of positive solutions of a degenerate quasilinear two point boundary value problem is investigated for the generalization of earlier results concerning the nondegenerate case with convex nonlinearity suitably defined p convex nonlinearities are considered strictly p convex c2 functions having a non negative root are classified according to the shape of the bifurcation diagram of positive solutions versus the length of the interval we have uniqueness when f 0 0 and 0 1 or 2 solutions when f 0 0 similarly to the non degenerate case provided that the number of solutions is finite however now there may also occur a continuum of solutions connected to a dead core type phenomenon the proof of our results relies on the shooting method for the characterization of the shape of the time map in contrast to the non degenerate case the shooting method does not determine directly the number of solutions owing to the lack of uniqueness of the corresponding ivp exact conditions on the uniqueness of the ivp and in the case of non uniqueness the number and types of its local solutions are given based on this all the positive solutions of the bvp can be compiled

exact structure of positive solutions for some p laplacian equations this paper establishes the exact multiplicities and properties of positive solutions for some second order differential equations involving p laplacian operator

uniqueness results for the one dimensional m laplacian considering superlinear nonlinearities abstract we study existence and uniqueness of positive solutions of the boundary value problem p u m 2 u f u in 0 1 u 0 u 1 0 where is a positive parameter m 1 and f 0 r is a continuous function which vanishes at most once in 0 assuming that f is superlinear at we study its behavior near zero to obtain uniqueness results which are proved using the shooting method

on the existence of bounded positive solutions for a class of singular bvps abstract we investigate the existence and properties of solutions to a second order singular ode we base ourselves on the variational approach which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences

exact number of positive solutions for a class of semipositone problems this paper is concerned with the boundary value problems y yp yq 0 and y 1 y 1 0 where p q 1 and 0 is a positive parameter we discuss the existence of positive solutions and give a complete study

analysis of positive radial solutions for singular superlinear p laplacian systems on the exterior of a ball abstract in this paper we study some well posedness properties of a positive radial solution pair u 1 u 2 to a singular boundary value problem in the form p u i k i x f i u j in r n b r 0 a i u i n c i u j u i u i 0 on b r 0 u i 0 as x where i j 1 2 i j p stands for the singular degenerate p laplacian p w div w p 2 w with 1 p n 0 a i 0 r 0 0 k i c r 0 0 and c i c 0 0 0 0 here the functions f i c 0 r i 1 2 satisfy a combined p superlinear growth at and possibly have singularities at 0 we establish an existence result for the case 0 multiplicity results of positive radial solutions for certain ranges of and nonexistence results of a positive radial solution for the case 1

uniqueness of positive radial solutions of a semilinear dirichlet problem in an annulus we establish the uniqueness of positive radial solutions of u u p u in b r 1 r 2 u 0 on b r 1 r 2 where b r 1 r 2 is an annulus and 0 r 1 r 2 in the following cases a n 3 4 and 1 p n n 2 b n 5 6 7 8 and 1 p p 0 n for some p 0 n n n 2 earlier to this result the uniqueness has been obtained by coffman for n 3 and 1 p 3 and by yadava for p n 2 n 2 and n 3

on non radially symmetric bifurcation in the annulus we discuss the radially symmetric solutions and the non radially symmetric bifurcation of the semilinear elliptic equation u 2 eu 0 in and u 0 on where x r2 a2 0 a the upper branch of radial solutions has a non radially symmetric bifurcation symmetry breaking at each k a k 1 as a 0 the radial solutions will tend to the radial solutions on the disk and 0 a 1 the critical number on the disk

computational complexities and streamfunction coordinates in this work we consider some of the computational aspects of viscous fluid flow through two dimensional curvilinear domains associated with the use of the von mises transformation in mapping a physical plane into a computational plane are some complexities that arise in the main part due to the infinite nature of the jacobian of the transformation some recommendations are made in this work to overcome some of the arising computational difficulties

on radial solutions for singular combined superlinear elliptic systems on annular domains abstract we prove the existence of a large positive solution to the system r n 1 1 u r n 1 f 1 v a r b r n 1 2 v r n 1 f 2 u a r b u a 0 u b v a 0 v b where a 0 is a small positive parameter f i 0 r are continuous and lim z 1 1 f 1 c 2 1 f 2 z z for all c 0

classification of bifurcation diagrams of a p laplacian dirichlet problem with examples abstract we study bifurcation diagrams of positive solutions of the p laplacian dirichlet problem p u x f u x 0 1 x 1 u 1 u 1 0 where p y y p 2 y p u is the one dimensional p laplacian and p 1 and 0 are two bifurcation parameters assume that f u g u h u where g h c 0 c 2 0 satisfy hypotheses h1 h5 presented herein for different values p with 1 p 2 and with p 2 we give a classification of totally six different bifurcation diagrams we prove that on the u plane each possible bifurcation diagram consists of exactly one curve with exactly one turning point where the curve turns to the right hence we are able to determine the exact multiplicity of positive solutions in addition for 1 p 2 and for p 2 we give interesting examples f u k u p 1 u q u r satisfying r q p 1 and k 0 and show complete evolution of bifurcation diagrams as evolution parameter k varies from 0 to

uniqueness of positive radial solutions for dirichlet problems on annular domains abstract this paper deals with the uniqueness of positive radial solutions to dirichlet problems on annular domains in r n n 3 as an application we can obtain the results to equation u u p 1 u 0 0 where p 1 1 0 0 0 and 1 0 0

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

the three solutions theorem for p laplacian boundary value problems abstract the three solutions theorem is established for p laplacian boundary value problems in the presence of two pairs of lower and upper solutions which are well ordered by the relationship between the lower and upper solutions and degree theory in addition an application of the three solutions theorem is given

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

positive solutions for a higher order four point boundary value problem with a p laplacian in this paper we study the existence of positive solutions of the following nth order four point boundary value problem with one dimensional p laplacian f p u n 1 h t f t u t u t u n 2 t 0 0 3 u i 0 0 0 i n 3 u n 1 0 au n 2 x 0 n 3 u n 1 1 bu n 2 h 0 n 3 where f p s s p 2s p 1 0 a 1 x 0 b 11 h 0 x h 1 by using a fixed point theorem in cones the existence of a positive solution and multiple positive solutions is obtained also at the end of this paper we present a generalization of this problem

positive solutions of systems of singular hammerstein integral equations with applications to semilinear elliptic equations in annuli abstract the existence of multiple positive solutions of systems of singular hammerstein integral equations is studied where the nonlinearities involved are allowed to have singularities in their second variables and satisfy weaker conditions involving the first eigenvalues of the corresponding linear hammerstein integral operators such systems contain some mathematical models arising in science and engineering applications are given to the existence of multiple positive radial solutions of systems of semilinear singular elliptic equations in annuli on which to the best of our knowledge there has been little study

uniqueness of radially symmetric positive solutions for delta u u u p in an annulus in this article we prove that the semi linear elliptic partial differential equation u u upin u 0in u 0on possesses a unique positive radially symmetric solution here p 1 and is the annulus x rn a x b with n 2 0 a b we also show the positive solution is non degenerate

first order accurate finite difference schemes for boundary vorticity approximations in curvilinear geometries in this work we develop first order accurate forward finite difference schemes for the first derivative on both a uniform and a non uniform grid the schemes are applied to the calculation of vorticity on a solid wall of a curvilinear two dimensional channel the von mises coordinates are used to transform the governing equations and map the irregular domain onto a rectangular computational domain vorticity on the solid boundary is expressed in terms of the first partial derivative of the square of the speed of the flow in the computational domain and the derived finite difference schemes are used to calculate the vorticity at the computational boundary grid points using combinations of up to five computational domain grid points this work extends previous work awartani et al 2005 3 in which higher order schemes were obtained for the first derivative using up to four computational domain grid points the aim here is to shed further light onto the use of first order accurate non uniform finite difference schemes that are essential when the von mises transformation is used results show that the best schemes are those that use a natural sequence of non uniform grid points it is further shown that for non uniform grid with clustering near the boundary solution deteriorates with increasing number of grid points used by contrast when a uniform grid is used solution improves with increasing number of grid points used

positive solution for singular boundary value problems abstract a sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u t f t u t 0 0 u 0 u 1 0 is constructed where f 0 1 0 0 is continuous f t u is locally lipschitz continuous and f t u u is strictly decreasing in u 0 for each t 0 1

an elementary proof of the uniqueness of positive radial solutions of a quasilinear dirichlet problem we consider the quasilinear elliptic equation text div left nabla u m 2 nabla u right u p lambda u m 2 u in in b where b is a ball or an annulus in n 1 m n p is a positive real number and e using a generalized poho aev type variational identity of ni serrin or pucci and serrin and an elementary calculus lemma we establish uniqueness of positive radial solutions for the dirichlet boundary condition if either left text i right b text is a ball lambda underset raise0 3em hbox smash scriptscriptstyle geqslant text 0 1 p underset raise0 3em hbox smash scriptscriptstyle leqslant frac mn n m text for m n text and 1 p infty text for m n text or left text ii right b text is an annulus lambda in mathbb r text and p frac mn n m

eigenvalues and eigenfunctions of discrete conjugate boundary value problems abstract we consider the following boundary value problem 1 n p n y f k y y n 1 y n 2 0 k m i y 0 0 0 i p 1 i y m n i 0 0 i n p 1 where 1 p n 1 is fixed and 0 a characterization of the values of is carried out so that the boundary value problem has a positive solution next for 1 criteria are developed for the existence of two positive solutions of the boundary value problem in addition for particular cases we also offer upper and lower bounds for these positive solutions several examples are included to dwell upon the importance of the results obtained

uniqueness of positive radial solutions for quasilinear elliptic equations in an annulus abstract extending a previous result of tang 1 we prove the uniqueness of positive radial solutions of p u f u 0 subject to dirichlet boundary conditions on an annulus in r n with 2 p n under suitable hypotheses on the nonlinearity f this argument also provides an alternative proof for the uniqueness of positive solutions of the same problem in a finite ball see 9 in the complement of a ball or in the whole space r n see 10 3 11

a global bifurcation result for a semilinear elliptic equation abstract we consider the problem u u p u in a u 0 in a u 0 on a where a is an annulus of r n n 2 p 1 and 0 recent results gladiali et al 2009 5 ensure that there exists a sequence of values of the exponent p k at which nonradial bifurcation from the radial solution occurs we prove the existence of global branches of nonradial solutions bifurcating from the curve of radial ones

on eigenvalue intervals and twin eigenfunctions of higher order boundary value problems abstract in this paper we shall consider the boundary value problem y n q t y y 1 y n 2 p t y y 1 y n 2 n 2 t 1 1 y i 0 0 0 i n 3 y n 2 0 y n 1 0 0 yy n 2 1 y n 1 1 0 where 0 and are constants satisfying 0 0 0 and 0 intervals of are determined to ensure the existence of a positive solution of the boundary value problem for 1 we shall also offer criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are obtained for special cases several examples are included to dwell upon the importance of the results obtained

on the existence of positive radial solutions for nonlinear elliptic equations in annular domains abstract we study the existence of positive radially symmetric solutions of u g x f u 0 in annulus with dirichlet dirichlet neumann boundary conditions we show that the equation has a positive radial solution on any annulus if f and f are positive and f is superlinear at 0 and

classification and evolution of bifurcation curves for a multiparameter p laplacian dirichlet problem abstract we study the classification and evolution of bifurcation curves for the multiparameter p laplacian dirichlet problem p u x u q k 1 n a k u r k 1 0 1 x 1 q 0 0 r 1 r 2 r n n 2 a k 0 for k 1 2 n u 1 u 1 0 where p 1 p y y p 2 y p u is the one dimensional p laplacian and 0 is a bifurcation parameter and q 0 is an evolution parameter we give a classification of totally five qualitatively different bifurcation curves for different q 0 more precisely we prove that on the u plane each bifurcation curve is either a monotone curve if q 0 p 1 r n p 1 or has exactly one turning point where the curve turns to the right if q p 1 r n p 1 hence the problem has at most two positive solutions for each 0 we also show evolution of five bifurcation curves as q varies from 0 to

remarks on time map for quasilinear equations abstract we present two different generalizations of r schaaf s 1990 18 time map formula to quasilinear equations including the case of p laplacian we give conditions for monotonicity and for convexity of the time map which imply uniqueness or multiplicity results for the corresponding dirichlet boundary value problem our time map formulas can be also used for effective computations of the global solution curves

existence uniqueness and nondegeneracy of positive solutions of semilinear elliptic equations we study positive solutions of the dirichlet problem a u x f u x 0 x d u x o x e ad where d is an n ball we find necessary and sufficient conditions for solutions to be nondegenerate we also give some new existence and uniqueness theorems in this paper we study positive solutions of the dirichlet problem au x f u x o x f2

on the existence of positive solutions and their continuous dependence on functional parameters for some class of elliptic problems we discuss the existence and the dependence on functional parameters of solutions of the dirichlet problem for a kind of the generalization of the balance of a membrane equation since we shall propose an approach based on variational methods we treat our equation as the euler lagrange equation for a certain integral functional j we will not impose either convexity or coercivity of the functional we develop a duality theory which relates the infimum on a special set x of the energy functional associated with the problem to the infimum of the dual functional on a corresponding set xd the links between minimizers of both functionals give a variational principle and in consequence their relation to our boundary value problem we also present the numerical version of the variational principle it enables the numerical characterization of approximate solutions and gives a measure of a duality gap between primal and dual functional for approximate solutions of our problem

double positive solutions of n p boundary value problems for higher order difference equations abstract we shall provide existence criteria for double positive solutions of the n p boundary value problem n y f k y y n 2 y g k y y n 1 y n 1 k n i y 0 0 0 i n 2 p y n n p 0 where n 2 and 0 p n 1 is fixed upper and lower bounds for the two positive solutions are also established for a particular boundary value problem when n 2 several examples are included to dwell upon the importance of the results obtained

uniqueness and exact multiplicity of solutions for a class of dirichlet problems abstract we apply the monotone separation of graphs technique of l a peletier and j serrin l a peletier j serrin uniqueness of positive solutions of semilinear equations in r n arch ration mech anal 81 2 1983 181 197 l a peletier j serrin uniqueness of nonnegative solutions of semilinear equations in r n j differential equations 61 3 1986 380 397 as developed further by l erbe and m tang l erbe m tang structure of positive radial solutions of semilinear elliptic equations j differential equations 133 2 1997 179 202 to the question of exact multiplicity of positive solutions for a class of semilinear equations on a unit ball in r n we also observe that using p pucci and j serrin p pucci j serrin uniqueness of ground states for quasilinear elliptic operators indiana univ math j 47 2 1998 501 528 improvement of a certain identity of l erbe and m tang l erbe m tang structure of positive radial solutions of semilinear elliptic equations j differential equations 133 2 1997 179 202 produces a short proof of l erbe and m tang l erbe m tang structure of positive radial solutions of semilinear elliptic equations j differential equations 133 2 1997 179 202 result on the uniqueness of positive solution of 1 p q n 2 n 2 u u p u q 0 for x 1 u 0 when x 1

renormalization of feynman integrals on the lattice a perturbative renormalization procedure is proposed which applies to massive field theories on a space time lattice and is analogous to the bphz finite part prescription for continuum feynman integrals the renormalized perturbation theory is shown to be universal i e under very natural assumptions the continuum limit exists and is independent of the details of the lattice action

positive solutions of quasilinear boundary value problems abstract this paper deals with the existence of positive solutions for the boundary value problem formula formula where f is either superlinear or sublinear at and f t 0 may be negative and p is a positive continuous function the results extend several known results for semilinear equations our approach is based on fixed point theory for completely continuous operators which leave invariant a suitable cone in a banach space of continuous functions

exact multiplicity of solutions and s shaped bifurcation curves for the p laplacian perturbed gelfand problem in one space variable abstract we study exact multiplicity of positive solutions and the bifurcation curve of the p laplacian perturbed gelfand problem from combustion theory p u x exp a u a u 0 1 x 1 u 1 u 1 0 where p 1 p y y p 2 y p u is the one dimensional p laplacian 0 is the frank kamenetskii parameter u x is the dimensionless temperature and the reaction term f u exp a u a u is the temperature dependence obeying the arrhenius reaction rate law we find explicitly a a p 0 such that if the activation energy a a then the bifurcation curve is s shaped in the u plane more precisely there exist 0 such that the problem has exactly three positive solutions for exactly two positive solutions for and and a unique positive solution for 0 and

perturbative renormalization of massless φ 4 4 with flow equations perturbative renormalizability proofs in the wilson polchinski renormalization group framework based on flow equations were so far restricted to massive theories here we extend them to euclidean massless 4 4 as a by product of the proof we obtain bounds on the singularity of the green functions at exceptional momenta in terms of the exceptionality of the latter these bounds seem to be new and are quite sharp

exact multiplicity results for a p laplacian problem with concave convex concave nonlinearities we study the exact number of positive solutions of a two point dirichlet boundary value problem involving the p laplacian operator we consider the case p 2 as well as the case p 1 when the nonlinearity f satisfies f 0 0 and has two distinct simple positive zeros and such that f changes sign exactly twice on 0 note that we may allow that f changes sign more than twice on 0 some interesting examples of quartic polynomials are given in particular for f u u2 u 1 u 2 we study the evolution of the bifurcation curves of the p laplacian problem as p increases from 1 to infinity and hence are able to determine the exact multiplicity of positive solutions for each p 1

positive solutions and nonlinear eigenvalue problems for third order difference equations first solutions that lie in a cone intersected with an annular type region are obtained for the third order difference equation 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 in the cases that f is either superlinear or sublinear the second part is devoted to determining values of for which there exist positive solutions of 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 when both limx 0 f x x and limx f x x exist as positive real numbers

uniqueness of sign changing radial solutions for δu u u p 1u 0 in some ball and annulus abstract the following dirichlet problem u u u p 1 u 0 in u 0 on is considered where is either an annulus or a ball in r n and p 1 the uniqueness of radial solutions having exactly k 1 nodes is shown for the following cases is a sufficiently thin annulus is a certain small ball n 4 and 1 p n n 2 is the unit ball n 3 and 1 p 3 is any annulus or any ball but p 1 is sufficiently close to 1 and n 3 5 or 7

positive solutions of semipositone higher order differential equations on time scales abstract in this paper we are concerned with the following 2 n th order differential equations on time scales 1 n y 2 n t g t f t y t t a b y 2 i a i 1 y 2 i 1 a i 1 y 2 i i 1 y 2 i y 2 i b 0 i n 1 where a b n 1 i 0 1 i b a i a i 0 i b i i 1 a i b i 1 2 n the functions g a b 0 and f a b 0 are continuous or g is singular at t a and or t b we obtain some properties and sharp estimates of the corresponding green s function and investigate the existence of positive solutions of the semipositone problems for 2 n order differential equations by the use of the property of green s function variable transformation and the fixed point index theorem

on the existence of multiple solutions of the boundary value problem for nonlinear second order differential equations abstract we consider the boundary value problem for nonlinear second order differential equations of the form u a x f u 0 0 u 0 u 1 0 we establish the precise condition concerning the behavior of the ratio f s s at infinity and zero for the existence of solutions with prescribed nodal properties then we derive the existence and the multiplicity of nodal solutions to the problem our argument is based on the shooting method together with the strum s comparison theorem the results obtained here can be applied to the study of radially symmetric solutions of the dirichlet problem for semilinear elliptic equations in annular domains

orbital stability of standing waves for semilinear wave equations with indefinite energy the orbital stability of standing waves for semilinear wave equations is studied in the case that the energy is indefinite and the underlying space domain is bounded or a compact manifold or whole r n with n 2 the stability is determined by the convexity on of the lowest energy d of standing waves with frequency the arguments rely on the conservation of energy and charge and the construction of suitable invariant manifolds of solution flows

a power counting theorem for feynman integrals on the lattice a convergence theorem is proved which states sufficient conditions for the existence of the continuum limit for a wide class of feynman integrals on a space time lattice a new kind of a uv divergence degree is introcduced which allows the formulation of the theorem in terms of power counting conditions

existence and nonexistence of positive radial solutions for some semilinear elliptic problems in annular domains au f x u 0 in s u 0 on xj when n is some annulus and the above conditions in 4 29 are not necessarily satisfied in fact in our main result theorem 2 4 f is not necessarily c lim f t u u may not exist or may be u rn finite and f t u could be zero for u in some finite interval 0 p we also allow lim f t u u 0 corollary 2 6 and lim f t u u may not exist in example 2 3 below u o u 0 neither lim f u u nor lim f u u exists on the other hand we show that u 0 u m

the existence and uniqueness of bound state solutions of a semi linear equation we investigate the existence and uniqueness of bounded radially symmetric solutions in r3 of uf u 0 where f u is continuous piecewise linear and has three distinct real zeros we give a detail

elliptic equations of order 2m in annular domains in this paper we study the existence of positive radial solutions for some semilinear elliptic problems of order 2m in an annulus with dirichlet boundary conditions we consider a nonlinearity which is either sublinear or the sum of a sublinear and a superlinear term

uniqueness of positive solutions of a class of o d e with robin boundary conditions abstract we study the uniqueness of positive solutions of the boundary value problem u h t u f t u 0 t a b u a 0 u b 0 where 0 a b h c 0 r and f c 1 0 0 0 satisfy suitable conditions the proof of our main result is based upon the shooting method and the sturm comparison theorem

an application of topological transversality to non positive higher order difference equations in this paper we shall provide sufficient conditions on the non positive function i u 1 u n 1 so that the boundary value problem bvp given by e d nu i m i u i du i d n 2 i 0 and bc d mu 0 0 0 m n 3 a d n 2 0 b d n 1u 0 0 c d n 2u t 1 d d n 1u t 1 0 has at least one positive solution

existence of positive solutions for boundary value problem of second order fde abstract we use a fixed point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second order functional differential equation fde with the form y t r t y t 0 0 y t y t t r t 0 y t y t n t 1 t 1 a where y t y t for a we allow that r t has the singularity at the endpoints t 0 and t 1 of 0 1 our results include the situations that f is either superlinear or sublinear

existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains abstract this paper is concerned with the problem of elliptic equations in annular domains involving derivative terms using nonlinear analysis methods some results regarding existence of solutions are established more precisely at least one radial solution is obtained basing on schauder s fixed point theorem and contraction mapping theorem respectively some iterative technique is also applied which allows us to overcome difficulties that the nonlinearity is related to derivative terms

a convergence theorem for lattice feynman integrals with massless propagators it is shown that for non vanishing lattice spacing conventional infrared power counting conditions are sufficient for convergence of lattice feynman integrals with zero mass propagators if these conditions are supplemented by ultraviolet convergence conditions the continuum limit of such a diagram exists and is universal

renormalization of lattice feynman integrals with massless propagators a renormalization procedure is proposed which applies to lattice feynman integrals containing zero mass propagators and is analogous to the bphzl renormalization procedure for continuum feynman integrals the renormalized diagrams are infrared convergent for non exceptional external momenta if the vertices of the theory satisfy a general infrared constraint under the same conditions as in the massive case 4 the continuum limit of the renormalized theory exists and is independent of the details of the lattice action

the existence of positive solutions for the sturm liouville boundary value problems abstract for the sturm liouville boundary value problem p t u t f t u t 0 0 t 1 1 u 0 1 p 0 u 0 0 2 u 1 2 p 1 u 1 0 where 0 we shall use a fixed point theorem in a cone to obtain the existence of positive solutions for on a suitable interval