liouville theorem for elliptic equations with nonlinear boundary value conditions and finite morse indices abstract in this paper we study the nonexistence result for the following nonlinear elliptic equation with nonlinear boundary value condition u u p 1 u in r n u u q 1 u on r n if 1 p n 2 n 2 1 q n n 2 and p q n 2 n 2 n n 2 then we will show that this problem does not possess nontrivial bounded solution with finite morse index

elliptic problems with nonlinearities indefinite in sign abstract let r n n 3 be a bounded open set with smooth boundary and r we study the dirichlet problem formula with 1 q p and h k l nonnegative functions we prove existence nonexistence and multiplicity results depending on and according to the integrability properties of the ratio k p 1 h q 1

three state cyclic voter model extended with potts energy the cyclically dominated voter model on a square is extended by taking into consideration the variation of potts energy during the nearest neighbor invasions we have investigated the effect of surface tension on the self organizing patterns maintained by the cyclic invasions a geometrical analysis is also developed to study the three color patterns these investigations clearly indicate that in the voter model limit the pattern evolution is governed by the loop creation due to the overhanging during the interfacial roughening conversely in the presence of surface tension the evolution is governed by spiral formation whose geometrical parameters depend on the strength of cyclic dominance

four classes of interactions for evolutionary games the symmetric four strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices among these basis games four classes can be distinguished as it is already found for the three strategy games the games with self dependent cross dependent payoffs are characterized by matrices consisting of uniform rows columns six of 16 basis games describe coordination type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock paper scissors games in the absence of cyclic components the game is a potential game and the potential matrix is evaluated the main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games

trapping and cascading of eigenvalues in the large coupling limit we consider eigenvaluese of the hamiltonianh v w w compactly supported in the limit forw 0 we find monotonic convergence ofe to the eigenvalues of a limiting operatorh associated with an exterior dirichlet problem and we estimate the rate of convergence for 1 dimensional systems in 1 dimensional systems withw 0 or withw changing sign we do not find convergence instead we find a cascade phenomenon in which as each eigenvaluee stays near a dirichlet eigenvalue for a long interval of lengtho sqrt lambda of the scaling range quickly drops to the next lower dirichlet eigenvalue stays there for a long interval drops again and so on as a result for most large values of the discrete spectrum ofh is close to that ofe but when reaches a transition region the entire spectrum quickly shifts down by one we also explore the behavior of several explicit models as

monomial golod quotients of exterior algebras it is proved that for any set m of squarefree monomials in the variables x1 xn the algebra a k x1 xn m is golod if and only if the algebra b e x1 xn m is golod where e is the exterior algebra this is proved by showing the equivalence of the extremality of the poincare series of a and b

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

a priori bounds nodal equilibria and connecting orbits in indefinite superlinear parabolic problems we consider the dynamics of the semiflow associated with a class of semilinear parabolic problems on a smooth bounded domain posed with homogeneous dirichlet boundary conditions the distinguishing feature of this class is the indefinite superlinear but subcritical growth of the nonlinearity at infinity we present new a priori bounds for global semiorbits that enable us to give dynamical proofs of known and new existence results for equilibria in addition we can prove the existence of connecting orbits in many cases one advantage of our approach is that the parabolic semiflow is naturally order preserving in contrast to pseudo gradient flows considered when using variational methods therefore we can obtain much information on nodal properties of equilibria that was not known before

multibump nodal solutions for an indefinite superlinear elliptic problem abstract we define some nehari type constraints using an orthogonal decomposition of the sobolev space h 0 1 and prove the existence of multibump nodal solutions for an indefinite superlinear elliptic problem

solutions of superlinear elliptic equations and their morse indices we consider here solutions of semilinear second order elliptic equations with superlinear nonlinearities and we present some relationships between their morse indices and some qualitative properties in particular we show that for uo subcritical nonlinearities bounds on solutions are equivalent to bounds on their morse indices

applications of local linking to critical point theory we prove the existence of nontrivial critical points of functionals with a local linking at 0 applications to elliptic boundary value problems and to hamiltonian systems are given c 1995 academic press inc

solutions of fractional laplacian equations and their morse indices abstract in this paper we study the solutions of the following fractional laplacian equation s u f x u in u 0 in c under some assumptions on the nonlinearity we will show that the boundedness of solutions is equivalent to the finiteness of their morse indices we extend the result of bahri and lions 1992 1 from the laplacian equations to the fractional laplacian equations

bursts in three strategy evolutionary ordinal potential games on a square lattice abstract evolutionary potential games provide an analogy for equilibrium statistical physics under suitable conditions that is broken if cyclic components are added using monte carlo simulations we study the effect of weak cyclic perturbations on the equilibrium in a system of players located on a square lattice while the dynamics is controlled by a logit rule the pair interaction is composed of a symmetric three strategy coordination game of unit strength a weak self dependent term and a cyclic rock paper scissors component the self dependent component favors the first rock strategy which dominates the system behavior at low noises if the strength of the cyclic component is below a threshold value in the opposite case the predator of the first strategy paper rules the behavior at low noises while the first strategy can occasionally form growing domains bursts diminished after the appearance of the third one the variation of noise modifies the invasion velocities as well as the rate of nucleation processes and yields drastic changes in the strategy frequencies fluctuations average payoffs and spatio temporal patterns

a difference equation model for the hypercycle the paper presents a qualitative analysis of a system of n cyclically coupled difference equations x i x i c k i x i 1 c phi 1 with phi sum k i x i x i 1 which may be viewed as a discrete analogue of the hypercycle differential equation dot x i x i k i x i 1 phi these equations are of particular interest in the theory of self organization and biological evolution and have applications to the study of the social behaviour of animals

three state potts model in combination with the rock scissors paper game we study a three state potts model extended by allowing cyclic dominance between the states as exemplified in the rock scissors paper game monte carlo simulations are performed on a square lattice while varying the temperature and the strength of cyclic dominance it is shown that the critical phase transition from the disordered state to the ordered one is destroyed by the cyclic dominance which yields a self organizing pattern even at low temperatures the differences and similarities are discussed between the present model and half filled driven lattice gases with repulsive interaction

multiple solutions for a semilinear elliptic equation let ql be a bounded smooth domain in rn n 1 we consider the problem of finding nontrivial solutions to the elliptic boundary value problem au au h x iuip lu in q u 0 onoq where h 0 h 0 is holder continuous on q and p 1 a are constants let qlo denote the interior of the set where h vanishes in q we assume h 0 a e on q k1o and consider the eigenvalues ai k2 and ai 0o of the dirichlet problem in q and qlo respectively we prove that no nontrivial solution of the equation exists if a satisfies for some k 1 ak 90 k 1 a satisfies as ql 1 we consider the problem of finding nontrivial solutions to the elliptic boundary value problem 0 1 au au h x iuip u in q 0 2 u 0 on aq where h is a nonnegative not identically zero holder continuous function defined on q and p 1 a are constants ouyang 5 studied existence and uniqueness of positive solutions to problem 0 1 0 2 and also of its corresponding analogue on a compact riemannian manifold that paper mainly focused on studying the effect of vanishing of the received by the editors october 13 1993 and in revised form october 24 1994 1991 mathematics subject classification primary 35j25 35j20

superlinear indefinite equations on the real line and chaotic dynamics abstract in this paper we are concerned with a differential equation of the form x c x q t g x 0 t a b where a b q has infinitely many zeros in a b and g is superlinear we prove the existence of solutions with prescribed nodal properties in the intervals of negativity and positivity of q when c 0 and q is periodic we show that the equation under consideration exhibits chaotic like dynamics

characterization of solutions having finite morse index for some nonlinear pde with supercritical growth abstract in this paper we study solutions of the equation u u p in r n where n 2 n 2 p p c n see 3 for the definition of p c n we first classify all solutions not necessarily bounded having finite morse index for r n or r n with dirichlet boundary condition when is a regular bounded domain of r n for a family of solutions with dirichlet boundary condition u n we prove that u n l is bounded if and only if the morse index sequence i u n of u n is bounded finally we prove the same result for other nonlinearities f x u which have similar growth respectively at

superlinear indefinite elliptic problems and pohoz aev type identities abstract we prove the existence of a nontrivial solution for a nonlinear elliptic problem u u a x g u with dirichlet boundary condition on a bounded domain where g is superlinear both at zero and at infinity a x changes sign and 0

nontrivial solutions of operator equations and morse indices of critical points of min max type on montre que si les hypotheses du theoreme de point selle sont satisfaites si dim y 2 et si f 1 c contient seulement des points critiques non degeneres alors f 1 c contient au moins un point critique u 0 tel que 2 indice de morse u 0 dim y

liouville theorem for robin boundary value problems and finite morse indices in this paper we study the nonexistence result of the following nonlinear elliptic equation with robin boundary condition u u p 1uin r n u cu 0on r n under some assumptions on c and p we will show that this problem does not possess nontrivial bounded solution with finite morse index

existence of solutions for a nonhomogeneous semilinear elliptic equation abstract for a bounded domain a bounded caratheodory function g in r p 1 and a nonnegative locally integrable function h in which is strictly positive in a set of positive measure we prove that contrarily with the case h 0 there exists a solution of the semilinear elliptic problem u u g x u h u p 1 u f in u 0 on for every r and f l 2

solutions of the mixed boundary problem and their morse indices abstract in this paper we study the solutions of the following mixed boundary problem u f x u in u 0 on 1 u 0 on 2 under some assumptions on the nonlinearity we will show that the boundedness of solutions is equivalent to the finiteness of their morse indices we extend the result of a bahri p l lions solutions of superlinear elliptic equations and their morse indices commun pure appl anal 45 1992 1205 1215 from the dirichlet boundary condition to the mixed boundary condition

nontrivial solutions of schrodinger equations with indefinite nonlinearities we prove the existence of nontrivial solutions for the schrodinger equation delta u v x u a gamma x f u in r n where f is superlinear and suberitical at zero and infinity respectively v is periodic and a x chances sign c 2007 elsevier inc all rights reserved

radial solutions of superlinear equations on ℝn part i global variational approach we present a global variational approach to the search for multiple nodal solutions u h 1 n to a class of elliptic equations of type u x f x u x x n where n 2 f is superlinear and subcritical and f x 0

on the positive solutions of semilinear equations δ ℎ 0 on the compact manifolds in this paper we study the existence nonexistence and uniqueness of positive solutions of semilinear equations u u hu p 0 on compact riemannian manifolds as well as on bounded smooth domains in r n with homogeneous dirichlet or neumann boundary conditions

analysis of quasi dynamic ordinary differential equations and the quasi dynamic replicator abstract we study the mathematical properties of the quasi dynamic ordinary differential equations defined empirically in chen et al 2019 in particular we show how the allometric scaling mentioned in that work emerges naturally from the generalized lotka volterra model under the quasi dynamic ordinary differential equations paradigm we then define and study the proportional quasi dynamic ordinary differential equations and discuss the relationship of this equation system to both the classical and discrete time replicator dynamics we prove asymptotic properties of these systems for large and small populations and show that there exist populations for which the proportion of the population varies cyclically as a function of total logarithmic population size

transition matrix model for evolutionary game dynamics we study an evolutionary game model based on a transition matrix approach in which the total change in the proportion of a population playing a given strategy is summed directly over contributions from all other strategies this general approach combines aspects of the traditional replicator model such as preserving unpopulated strategies with mutation type dynamics which allow for nonzero switching to unpopulated strategies in terms of a single transition function under certain conditions this model yields an endemic population playing non nash equilibrium strategies in addition a hopf bifurcation with a limit cycle may occur in the generalized rock scissors paper game unlike the replicator equation nonetheless many of the folk theorem results are shown to hold for this model

fourier decomposition of payoff matrix for symmetric three strategy games in spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries for the two strategy games this decomposition reproduces interactions characteristic to the ising model for the three strategy symmetric games the fourier components can be classified into four types representing games with self dependent and cross dependent payoffs variants of three strategy coordinations and the rock scissors paper rsp game in the absence of the rsp component the game is a potential game the resultant potential matrix has been evaluated the general features of these systems are analyzed when the game is expressed by the linear combinations of these components