a critical p biharmonic system with negative exponents abstract in this paper we are devoted to the study of critical p biharmonic system with a parameter which involves strongly coupled critical nonlinearities and negative exponents we prove that there exists a positive constant such that the above problem admits at least two solutions if 0

on a liouville type equation with sign changing weight in this paper we study the existence nonexistence and multiplicity of non negative solutions for the family of problems u a x e f x u u h 0 where is a bounded domain in r2 and 0 is a parameter the coefficient a x is allowed to change sign the techniques used in the proofs are a combination of upper and lower solutions the trudingermoser inequality and variational methods note that when f x u 0 the equation is of liouville type

infinitely many nodal solutions for nonlinear elliptic equations with combined nonlinearities and lack of symmetry abstract we present a new approach to studying a parametric nonlinear dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is concave i e p 1 sublinear near zero and convex i e p 1 superlinear near the reaction term is not assumed to be odd we show that for all small values of the parameter 0 the problem has infinitely many nodal solutions

local superlinearity and sublinearity for the p laplacian we study the existence nonexistence and multiplicity of positive solutions for a family of problems updelta p u f lambda x u u in w 0 1 p upomega where is a bounded domain in mathbb r n n p and 0 is a parameter the family we consider includes the well known nonlinearities of ambrosetti brezis cerami type in a more general form namely lambda a x u q b x u r where 0 leqslant q p 1 r leqslant p 1 here the coefficient a x is assumed to be nonnegative but b x is allowed to change sign even in the critical case preliminary results of independent interest include the extension to the p laplacian context of the brezis nirenberg result on local minimization in w 0 1 p text and c 0 1 a c 1 alpha estimate for equations of the form updelta p u h x u with h of critical growth a strong comparison result for the p laplacian and a variational approach to the method of upper lower solutions for the p laplacian

combined effects of concave and convex nonlinearities in elliptic equation on rn abstract in this paper we consider the existence of two positive solutions of the elliptic equation on r n with concave and convex nonlinearities

limits as p of p laplacian concave convex problems abstract we study the behavior as p of the sequel of positive weak solutions of the concave convex problem p div u p 2 u u q p u r p in u 0 in u 0 on where r n is a bounded domain 0 and the exponents q r satisfy lim p q p p 1 q lim p r p p 1 r with 0 q 1 r we characterize any positive uniform limit of a sequence of weak solutions of p as a viscosity solution of min u max u q u r u 0 in notice that the limit process decouples the nonlinearity we obtain existence non existence and global multiplicity of positive viscosity solutions of the limit problem in terms of the parameter

existence and multiplicity of solutions for a nonlocal problem with critical sobolev exponent abstract in this work we are interested in considering the following nonlocal problem a b u 2 d x u u 2 2 u u q 2 u x u 0 x where r n n 4 is a smooth bounded domain a 0 b 0 1 q 2 0 and 2 2 n n 2 is the critical sobolev exponent by using the variational method and the critical point theorem some existence and multiplicity results are obtained

on semilinear elliptic equations involving concave convex nonlinearities and sign changing weight function abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign changing weight function with the help of the nehari manifold we prove that there are at least two positive solutions for eq e f in bounded domains

modified dfa and dcca approach for quantifying the multiscale correlation structure of financial markets abstract we use multiscale detrended fluctuation analysis msdfa and multiscale detrended cross correlation analysis msdcca to investigate auto correlation ac and cross correlation cc in the us and chinese stock markets during 1997 2012 the results show that us and chinese stock indices differ in terms of their multiscale ac structures stock indices in the same region also differ with regard to their multiscale ac structures we analyze ac and cc behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly we choose s p500 nqci hsi and the shanghai composite index as representative samples for simplicity msdfa and msdcca results and average msdfa spectra for local scaling exponents lses for individual series are presented we find that the msdcca spectrum for lse cc between two time series generally tends to be greater than the average msdfa lse spectrum for individual series we obtain detailed multiscale structures and relations for cc between the four representatives msdfa and msdcca with secant rolling windows of different sizes are then applied to reanalyze the ac and cc vertical and horizontal comparisons of different window sizes are made the msdfa and msdcca results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained

nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity abstract we are concerned with existence nonexistence and multiplicity of nonnegative solutions for the elliptic problem u a x u q b x u p in u 0 on where is a bounded domain in r n r 0 q 1 p 2 1 and a b are bounded functions with b x 0 and a x changes its sign

positive solutions of superlinear elliptic equations abstract in this paper we study the existence of two positive solutions of superlinear elliptic equations without assuming the conditions which have been used in the literature to deduce either the p s condition or a priori bounds of positive solutions the first solution is proved as the minimal positive solution while the second one is obtained as the limit of a gradient flow whose starting point is properly chosen the dependence of the minimal solution upon a parameter is also considered

exact multiplicity and bifurcation diagrams of positive solutions of a one dimensional multiparameter prescribed mean curvature problem abstract we study the exact multiplicity and bifurcation diagrams of positive solutions u c 2 l l c l l of the one dimensional multiparameter prescribed mean curvature problem u x 1 u x 2 u p u q l x l u l u l 0 where 0 is a bifurcation parameter l 0 the radius of the one dimensional ball l l is an evolution parameter and 0 p q are two constants we prove that the problem has at most two positive solutions for any 0 p q and l 0 in addition if 0 p q q p p 1 2 p 1 we give a classification of totally three qualitatively different bifurcation diagrams on the u plane for any l 0 for any fixed p 0 and q q p p 2 2 2 p 3 we prove that there exist positive l l such that the bifurcation diagrams on the u plane are individually qualitatively different for the cases i 0 l l or l l ii l l iii l l l

quantification of heart rate variability by discrete nonstationary non markov stochastic processes we develop the statistical theory of discrete nonstationary non markov random processes in complex systems the objective of this paper is to find the chain of finite difference non markov kinetic equations for time correlation functions tcf in terms of nonstationary effects the developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of initial and final states and nonstationary normalized tcf using the projection operators technique we find the chain of finite difference non markov kinetic equations for discrete nonstationary tcf and for the set of nonstationary discrete memory functions mf s the last one contains supplementary information about nonstationary properties of the complex system on the whole another relevant result of our theory is the construction of the set of dynamic parameters of nonstationarity which contains some information of the nonstationarity effects the full set of dynamic spectral and kinetic parameters and kinetic functions tcf short mf s statistical spectra of non markovity parameter and statistical spectra of nonstationarity parameter has made it possible to acquire the in depth information about discreteness non markov effects long range memory and nonstationarity of the underlying processes the developed theory is applied to analyze the long time holter series of rr intervals of human ecg s we had two groups of patients the healthy ones and the patients after myocardial infarction in both groups we observed effects of fractality standard and restricted self organized criticality and also a certain specific arrangement of spectral lines the received results demonstrate that the power spectra of all orders n 1 2 mf m n t exhibit the neatly expressed fractal feat ures we have found out that the full sets of non markov discrete and nonstationary parameters can serve as reliable and powerful means of diagnosis of the cardiovascular system states and can he used to distinguish healthy data from pathologic data

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

combined effects in nonlinear problems arising in the study ofanisotropic continuous media the paper deals with the study of a lane emden fowler equation with dirichlet boundary condition and variable potential functions the analysis developed in this paper combines monotonicity methods with variational arguments

on a dirichlet problem with p q laplacian and parametric concave convex nonlinearity abstract a homogeneous dirichlet problem with p q laplace differential operator and reaction given by a parametric p convex term plus a q concave one is investigated a bifurcation type result describing changes in the set of positive solutions as the parameter 0 varies is proven since for every admissible the problem has a smallest positive solution u both monotonicity and continuity of the map u are studied

effect of nonlinear filters on detrended fluctuation analysis when investigating the dynamical properties of complex multiple component physical and physiological systems it is often the case that the measurable system s output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms instead the output signal is often a linear or nonlinear function of the quantity of interest here we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal using the detrended fluctuation analysis dfa which has been shown to accurately quantify power law correlations in nonstationary signals specifically we study the effect of three types of transforms i linear y i a x i b ii nonlinear polynomial y i a x k i and iii nonlinear logarithmic y i log x i delta filters we compare the correlation and scaling properties of signals before and after the transform we find that linear filters do not change the correlation properties while the effect of nonlinear polynomial and logarithmic filters strongly depends on a the strength of correlations in the original signal b the power k of the polynomial filter and c the offset delta in the logarithmic filter we further apply the dfa method to investigate the apparent scaling of three analytic functions i exponential exp x a ii logarithmic log x a and iii power law x a lambda which are often encountered as trends in physical and biological processes while these three functions have different characteristics we find that there is a broad range of values for parameter a common for all three functions where the slope of the dfa curves is identical we further note that the dfa results obtained for a class of other analytic functions can be reduced to these three typical cases we systematically test the performance of the dfa method when estimating long range power law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider

study of the singular anharmonic potentials by means of the analytic continuation method here we study the singular anharmonic potentials by applying the analytic continuation method of holubec and stauffer 1985 in order to do that we have developed several approximations to the problem because this method cannot be applied when the solution has essential singularities at any point of its domain all the options here shown have the same precision giving us the eigenvalues correct to all the decimal places provided by the computer

existence of solutions for perturbed fractional p laplacian equations abstract the purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional p laplacian operator as follows p s u v x u p 2 u a x u r 2 u b x u q 2 u in r n where is a real parameter p s is the fractional p laplacian operator with 0 s 1 p p r min q p s and v a b r n 0 are three positive weights using variational methods we obtain nonexistence and multiplicity results for the above mentioned equations depending on and according to the integrability properties of the ratio a q p b r p our results extend the previous work of autuori and pucci 2013 5 to the fractional p laplacian setting furthermore we weaken one of the conditions used in their paper hence the results of this paper are new even in the fractional laplacian case

critical point theory on partially ordered hilbert spaces we develop some abstract critical point theory in order to prove that boundary value problems like the model problem formula on a bounded domain rn 2 p 2n n 2 have infinitely many sign changing solutions uk k n which are not comparable that is uk ul and uk ul change sign for k l we also show that there are no subsolutions u such that u uk for some k and u is positive somewhere a corresponding nonexistence result applies to supersolutions related results on the existence of sign changing solutions hold for other classes of nonlinearities

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

evaluating age related loss of nonlinearity degree in short term heartbeat series by optimum modeling dimension abstract detecting the alterations of nonlinearity in short term heartbeat dynamics has got the realistic meaning the paper first studies some short nonlinear series by predicting the series with a nonlinear autoregressive model then inspired by the fact that the optimum modeling dimension of the model can characterize the intrinsic dimensional feature of the dynamics the paper presents a new idea that the optimum modeling dimension can be taken to evaluate the nonlinearity degree of the original dynamics finally we apply this proposition to the heartbeat dynamics we study the short term heart interbeat interval series of a group of healthy subjects and have a comparison between the results of the young subjects and those of the old ones we find that the optimum modeling dimensions of the old subjects are smaller than those of the young ones it shows the nonlinearity degree decreases with aging

the nehari manifold for a semilinear elliptic system involving sign changing weight functions abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e with sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

multiple solutions to p laplacian problems with concave nonlinearities in this paper we study the p laplacian type elliptic problems with concave nonlinearities using some asymptotic behavior of f at zero and infinity three nontrivial solutions are established

nonlinear elliptic equations with an asymptotically linear reaction term abstract we examine nonlinear elliptic problems driven by the p laplacian and with a reaction term which asymptotically at exhibits a p 1 linear growth 1 p using tools from critical point theory and from morse theory we prove existence theorems and we provide information about the sign of the solutions

variational and perturbative schemes for a spiked harmonic oscillator a variational analysis of the spiked harmonic oscillator hamiltonian operator d2 dx2 x2 l l 1 x2 x where is a real positive parameter is reported in this work the formalism makes use of the functional space spanned by the solutions of the schrodinger equation for the linear harmonic oscillator hamiltonian supplemented by a dirichlet boundary condition and a standard procedure for diagonalizing symmetric matrices the eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system valid for positive and relatively large values of the coupling parameter additionally a large coupling perturbative expansion is carried out and the contributions up to fourth order to the ground state energy are explicitly evaluated numerical results are compared for the special case 5 2

compact sobolev embeddings and positive solutions to a quasilinear equation with mixed nonlinearities abstract in this paper we study the existence and multiplicity results of nontrivial positive solutions to the following quasilinear elliptic equation on r n when n 2 p u k x u r 1 v x u q 1 here k x v x 0 are suitable potentials 1 p r q and 0 is a parameter to study this problem some compact embedding results regarding m v q p r n l k r r n are proved that unify and extend some recent results of the author 12 13 14

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

effect of extreme data loss on long range correlated and anticorrelated signals quantified by detrended fluctuation analysis detrended fluctuation analysis dfa is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations to better identify the intrinsic correlation properties of real world signals where a large amount of data is missing or removed due to artifacts we investigate how extreme data loss affects the scaling behavior of long range power law correlated and anticorrelated signals we introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long range correlations the surrogate signals we generate are characterized by four parameters i the dfa scaling exponent alpha of the original correlated signal u i ii the percentage p of the data removed from u i iii the average length mu of the removed or remaining data segments and iv the functional form p l of the distribution of the length l of the removed or remaining data segments we find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90 in contrast the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost these observations are confirmed on two examples of real world signals human gait and commodity price fluctuations we further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales we find that for anticorrelated signals even 10 of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior in contrast positively correlated signals show no observable changes in the local scaling for up to 65 of data loss while for larger percentage of data loss the local scaling shows overestimated regions with higher local exponent at small scales followed by underestimated regions with lower local exponent at large scales finally we investigate how the scaling is affected by the average length probability distribution and percentage of the remaining data segments in comparison to the removed segments we find that the average length mu r of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value interestingly the scales where the maximum deviation occurs follow a power law relationship with mu r whereas the percentage of data loss determines the extent of the deviation the results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss

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

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

a nonlinear elliptic equation with critical exponent estimates for extremal values abstract in this work we study the values of p q the supremum of the set of related to existence and multiplicity of positive solutions of semilinear elliptic equations involving a critical sobolev exponent and establish uniform lower bounds for

magnitude and sign scaling in power law correlated time series a time series can be decomposed into two sub series a magnitude series and a sign series here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example we 6nd that time series having identical distributions and long range correlation properties can exhibit quite di8erent temporal organizations of the magnitude and sign sub series from the cases we study it follows that the long range correlations in the magnitude series indicate nonlinear behavior speci6cally our results suggest that the correlation exponent of the magnitude series is a monotonically increasing function of the multifractal spectrum width of the original series on the other hand the sign series mainly relates to linear properties of the original series we also show that the magnitude and sign series of the heart interbeat interval series can be used for diagnosis purposes c

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

normalized ground states for the nls equation with combined nonlinearities abstract we study existence and properties of ground states for the nonlinear schrodinger equation with combined power nonlinearities u u u q 2 u u p 2 u in r n n 1 having prescribed mass r n u 2 a 2 under different assumptions on q p a 0 and r we prove several existence and stability instability results in particular we consider cases when 2 q 2 4 n p 2 q p i e the two nonlinearities have different character with respect to the l 2 critical exponent these cases present substantial differences with respect to purely subcritical or supercritical situations which were already studied in the literature we also give new criteria for global existence and finite time blow up in the associated dispersive equation

multiplicity of positive solutions for p laplace equation with superlinear type nonlinearity abstract in this work we consider the problem p r p u u p u q u 0 in b r 0 u 0 on b r 0 where p 2 p np n p and b r 0 is the open ball of radius r centered about the origin in r n n 3 under the condition that p 1 q p 2 n p 1 we show that there exists r 0 such that p r admits atleast two solutions for all r r and no solution if r this extends the results of nonlinear anal tma 10 8 1986 755 to the case of p laplace equation

on elliptic problems involving critical hardy sobolev exponents and sign changing function abstract in this paper we deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical hardy sobolev exponent and a sign changing function some existence results are obtained by splitting the nehari manifold and by exploring some properties of the best hardy sobolev constant together with an approach developed by brezis and nirenberg

integral equations a tool to solve the schrodinger equation from the integral equation equivalent to the one dimensional schrodinger equation with the boundary conditions appropriate for a bound state problem an exact three point integration rule is derived the approximate evaluation of this rule by means of the euler mclaurin sum rule gives rise to various o h2 and o h4 integration methods associated with the different ways of splitting the starting equation into a free part and an interaction term the method is particularly useful to deal with the singularities of the potential

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

solving the 1 2 and 3 dimensional schrodinger equation for multiminima potentials using the numerov cooley method an extrapolation formula for energy eigenvalues as demonstrated with examples the numerov cooley algorithm can be applied to more complicated potentials especially multiminima potentials there are no stability problems in the classically forbidden regions an extrapolation formula for energy eigenvalues is deduced which gets an additional accuracy of 2 4 digits for energy eigenvalues this formula is checked as follows for one state of a double minimum potential which is used to approximate hydrogen bond potentials an analytical solution is given this solution is compared with numerical results also the accuracy of the eigenfunctions is checked computer dependent rounding errors cdc cyber 995 are estimated the eigenfunctions corresponding to 1 dimensional potentials v x x and v y y are used as basis functions for a perturbed 2 dimensional multiminima potential v x x v y y email protected x y for a 63 minima potential as an example the accuracy of the eigenvalues is 4 6 digits depending on the perturbation dv x y the computer time depending on the accuracy is tabulated for different potentials

nondegeneracy and uniqueness of positive solutions for robin problem of second order ordinary differential equations and its applications abstract this article studies positive solutions of robin problem for semi linear second order ordinary differential equations nondegeneracy and uniqueness results are proven for homogeneous differential equations necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations

radial solutions of dirichlet problems with concave convex nonlinearities abstract we prove the existence of a double infinite sequence of radial solutions for a dirichlet concave convex problem associated with an elliptic equation in a ball of r n we are interested in relaxing the classical positivity condition on the weights by allowing the weights to vanish the idea is to develop a topological method and to use the concept of rotation number the solutions are characterized by their nodal properties

finite difference approximate solutions for a mixed sub superlinear equation in ben mabrouk and ben mohamed 2006 a ben mabrouk m l ben mohamed on some critical and slightly super critical sub superlinear equations far east j appl math 23 1 2006 73 90 special volume of pdes a ben mabrouk m l ben mohamed nodal solutions for some nonlinear elliptic equations appl math comp in press doi 10 1016 j amc 2006 08 003 it has proved some theoretical results dealing with some boundary value problem du f u 0 in b and u 0 on b where b is a domain in r d with smooth boundary in the present paper we perform a difference scheme method to approximate the solution of a nonlinear evolutionary problem associated to the elliptic problem studied in ben mabrouk and ben mohamed 2006 we give at the end some numerical implementations based on a mixed sublinear superlinear term of the form f u u p email protected u q 1u

existence of nonnegative solutions for quasilinear elliptic equations with indefinite critical nonlinearities abstract we study the quasilinear elliptic equation div u u a x f u b x g u in with dirichlet boundary condition u 0 on where is a bounded domain in r n a x b x are sign changing continuous functions and g u has critical growth at infinity with respect to the principal part a nonnegative nontrivial solution is given under appropriate growth conditions on f u g u at 0 and

existence results for quasilinear elliptic exterior problems involving convection term and nonlinear robin boundary conditions abstract in this paper the authors establish the existence of solutions for a class of elliptic exterior problems involving convection terms and nonlinear robin boundary conditions the proof of the result is made by combining galerkin method with a priori estimates for this kind of problem

newton s method s basin of attraction for sign changing solutions of concave and convex nonlinearities abstract in this paper we will illustrate and visualize the chaotic behavior for solving the sign changing solutions of concave convex nonlinearities we propose contractor iteration algorithm and bifurcation method to improve the computation speed and avoid local convergence of newton raphson method by this method sign changing numerical solutions will be computed and visualized in various domains

on the singular second order elliptic equation abstract let m g be a smooth and compact riemannian manifold with dimensions n 3 this paper deals with the existence of nontrivial solutions for a nonlinear second order elliptic equation with a singular term and critical sobolev growth we provide a geometric application of this singular equation

scaling features of texts images and time series in the given paper we consider the scaling features of long letter sequences like human writings discretized images and discretized 3nancial data using several approaches we show that the symbolic strings and time series being analyzed have a complex multiscale structure and demonstrate di5erent scalings for large and small 6uctuations we discuss complex phenomena in the scaling behavior of partition functions in the case of high frequency dax future data c 2001 elsevier science b v all rights reserved

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

nonlinear analysis of cardiac rhythm fluctuations using dfa method abstract after a brief overview of classical techniques used to explore cardiac rhythm variability we show how the dfa method can help diagnose heart failure

existence and multiplicity results for quasilinear elliptic exterior problems with nonlinear boundary conditions abstract in this paper we study a class of quasilinear elliptic exterior problems with nonlinear boundary conditions existence of ground states and multiplicity results are obtained via variational methods

existence of infinitely many spike solutions for a critical henon type biharmonic equation abstract following the idea of wei and yan 32 with new ingredients to take care of the critical dimension n 5 we construct infinitely many solutions of the biharmonic equation 2 v x v n 4 n 4 in the unit ball of r n n 5 0 with the navier conditions v v 0 on the boundary

on the evolution and qualitative behaviors of bifurcation curves for a boundary value problem abstract we study the evolution and qualitative behaviors of bifurcation curves of positive solutions for u x u 1 sin u u p 1 x 1 u 1 u 1 0 where 0 is a bifurcation parameter and p 1 is an evolution parameter on the u plane we prove that the bifurcation curve has exactly one turning point where the curve turns to the left for p 2 it is a monotone curve for p 2 it has at least two turning points for 1 p p 1 2 cos 1 sin 1 1 2 cos 1 sin 1 1 629 and it has infinitely many turning points for p 1 hence we are able to determine the exact number of positive solutions in particular we give complete descriptions of the structure of bifurcation curves when p 2 we also give some numerical simulations of bifurcation curves for p 1

positive solutions of semilinear biharmonic equations with critical sobolev exponents in this paper we study the critical growth biharmonic problem with a parameter and establish uniform lower bounds for which is the supremum of the set of related to the existence of positive solutions of the biharmonic problem

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

the nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition abstract using the nehari manifold and fibering maps we prove the existence theorem of the nonlinear boundary problem u u u p 2 u for x u n u q 2 u for x on a bounded domain r n we discuss how the nehari manifold changes as changes and show how the existence of solutions depends on the properties of the nehari manifold

a complete classification of bifurcation diagrams of classes of multiparameter p laplacian boundary value problems we study the bifurcation diagrams of positive solutions of the multiparameter p laplacian problem p u x f u x 0 1 x 1 u 1 u 1 0 where p 1 p y y p 2y p u is the one dimensional p laplacian f u g u h u and 0 and 0 are two bifurcation parameters 0 and 0 are two given real numbers assuming that functions g and h satisfy hypotheses h1 h3 and h4a resp h1 h3 and h4b for fixed 0 resp 0 we give a classification of totally eight qualitatively different bifurcation diagrams we prove that on the u plane resp 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 right hence the problem has at most two positive solutions for each 0 resp 0 more precisely we prove the exact multiplicity of positive solutions in addition for all p 1 we give interesting examples which show complete evolution of bifurcation diagrams as resp varies

existence and asymptotic behavior of ground states for quasilinear singular equations involving hardy sobolev exponents abstract we study the existence and decaying rate of solutions for the quasilinear problem p u x f u x g u in r n u 0 in r n u x 0 where p stands for the p laplacian operator 1 p n r n 0 is continuous and not identically zero 0 is a parameter x is the euclidean norm of x 0 p f g 0 0 are continuous and nondecreasing f has sublinear growth and the hardy sobolev exponent p p n n p bounds the growth of g we deal with variational methods and the lower and upper solutions technique

on a nonlinear fourth order elliptic equation involving the critical sobolev exponent in this paper we use an algebraic topological argument due to bahri and coron to show how the topology of the domain influences the existence of positive solutions of the following problem involving the bilaplacian operator with the critical sobolev exponent 2u un 4 n 4 in u 0 in u u 0 on where is a bounded domain of rn n 5 with a smooth boundary

compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity we study the branch of semistable and unstable solutions i e those whose morse index is at most 1 of the dirichlet boundary value problem u f x 1 u 2 on a bounded domain n which models among other things a simple electrostatic microelectromechanical system mems device we extend the results of 11 relating to the minimal branch by obtaining compactness along unstable branches for 1 n 7 on any domain and for a large class of permittivity profiles f we also show the remarkable fact that powerlike profiles f x x can push back the critical dimension n 7 of this problem by establishing compactness for the semistable branch on the unit ball also for n 8 and as long as as a byproduct we are able to follow the second branch of the bifurcation diagram and prove the existence of a second solution for in a natural range in all these results the conditions on the space dimension and on the power of the profile are essentially sharp 2007 wiley periodicals inc

three positive solutions for dirichlet problems involving critical sobolev exponent and sign changing weight abstract in this paper we study the decomposition of the nehari manifold via the combination of concave and convex nonlinearities furthermore we use this result and the lusternik schnirelman category to prove that a semilinear elliptic equation involving a sign changing weight function has at least three positive solutions

four positive solutions for a semilinear elliptic equation involving concave and convex nonlinearities abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic equation with the help of the nehari manifold and the center mass function we prove that there are at least four positive solutions for a semilinear elliptic equation in a finite strip with a hole