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991.
We study the adaptive dynamics of predator–prey systems modeled by a dynamical system in which the traits of predators and prey are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the mutational change tends to 0, the system does not exhibit long term prey coexistence and the trait of the resident prey type converges to the solution of an ODE. When only the predators are allowed to evolve, coexistence of predators occurs. In this case, depending on the parameters being varied, we see that (i) the number of coexisting predators remains tight and the differences in traits from a reference species converge in distribution to a limit, or (ii) the number of coexisting predators tends to infinity, and we calculate the asymptotic rate at which the traits of the least and most “fit” predators in the population increase. This last result is obtained by comparison with a branching random walk killed to the left of a linear boundary and a finite branching–selection particle system. 相似文献
992.
We study existence, uniqueness and approximation of solutions of stochastic differential equations with jump reflection at time-dependent barriers. The basic idea in proofs consists in applying new existence and stability theorems on deterministic one-dimensional Skorokhod problem. Our results are new even in the classical case of one reflecting barrier. 相似文献
993.
A. Amini-Harandi M. Fakhar J. Zafarani 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):2891-2895
A new generalized set-valued contraction on topological spaces with respect to a measure of noncompactness is introduced. Two fixed point theorems for the KKM type maps which are either generalized set-contraction or condensing ones are given. Furthermore, applications of these results for existence of coincidence points and maximal elements are deduced. 相似文献
994.
Valeri Obukhovskii 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1715-1728
We consider a semilinear functional differential inclusion with infinite delay and impulse characteristics in a Banach space assuming that its linear part is a non-densely defined Hille-Yosida operator. We assume that the multivalued nonlinearity of upper Carathèodory or almost lower semicontinuous type satisfies a regularity condition expressed in terms of the measures of noncompactness. We apply the theory of integrated semigroups and the theory of condensing multivalued maps to obtain local and global existence results. The application to an optimization problem for an impulsive feedback control system is given. 相似文献
995.
Reinhard Farwig Hermann Sohr 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1459-1465
There are only very few results on the existence of unique local in time strong solutions of the Navier-Stokes equations for completely general domains Ω⊆R3, although domains with edges and corners, bounded or unbounded, are very important in applications. The reason is that the Lq-theory for the Stokes operator A is available in general only in the Hilbert space setting, i.e., with q=2. Our main result for a general domain Ω is optimal in a certain sense: Consider an initial value and a zero external force. Then the condition is sufficient and necessary for the existence of a unique local strong solution u∈L8(0,T;L4(Ω)) in some interval [0,T), 0<T≤∞, with u(0)=u0, satisfying Serrin’s condition . Note that Fujita-Kato’s sufficient condition u0∈D(A1/4) is strictly stronger and therefore not optimal. 相似文献
996.
Sehie Park 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):1028-1042
The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. A KKM space is an abstract convex space satisfying the partial KKM principle and its “open” version. In this paper, we clearly derive a sequence of a dozen statements which characterize the KKM spaces and equivalent formulations of the partial KKM principle. As their applications, we add more than a dozen statements including generalized formulations of von Neumann minimax theorem, von Neumann intersection lemma, the Nash equilibrium theorem, and the Fan type minimax inequalities for any KKM spaces. Consequently, this paper unifies and enlarges previously known several proper examples of such statements for particular types of KKM spaces. 相似文献
997.
Mohammad Sal Moslehian Dorian Popa 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2792-2799
Suppose that X is a sequentially complete Hausdorff locally convex space over a scalar field K, V is a bounded subset of X, (an)n≥0 is a sequence in K?{0} with the property lim infn→∞|an|>1, and (bn)n≥0 is a sequence in X. We show that for every sequence (xn)n≥0 in X satisfying
998.
Edcarlos D. da Silva 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2451-2462
In this paper we establish the existence and multiplicity of solutions for a quasilinear elliptic problem under strong resonance conditions at infinity. In order to control the resonance we consider a new hypothesis on the nonlinear term. In all results we use Variational Methods, Critical Groups and the Morse Theory. 相似文献
999.
Let Ω be an open domain of class C2 contained in R3, let L2(Ω)3 be the Hilbert space of square integrable functions on Ω and let H[Ω]?H be the completion of the set, , with respect to the inner product of L2(Ω)3. A well-known unsolved problem is that of the construction of a sufficient class of functions in H which will allow global, in time, strong solutions to the three-dimensional Navier-Stokes equations. These equations describe the time evolution of the fluid velocity and pressure of an incompressible viscous homogeneous Newtonian fluid in terms of a given initial velocity and given external body forces. In this paper, we use the analytic nature of the Stokes semigroup to construct an equivalent norm for H, which provides strong bounds on the nonlinear term. This allows us to prove that, under appropriate conditions, there exists a number u+, depending only on the domain, the viscosity, the body forces and the eigenvalues of the Stokes operator, such that, for all functions in a dense set D contained in the closed ball B(Ω)?B of radius in H, the Navier-Stokes equations have unique, strong, solutions in C1((0,∞),H). 相似文献
1000.
Bang-Yen Chen 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3561-3571
In this paper we initiate the study of Lagrangian submanifolds in para-Kähler manifolds. In particular, we prove two general optimal inequalities for Lagrangian submanifolds of the flat para-Kähler manifold . Moreover, we completely classify Lagrangian submanifolds which satisfy the equality case of one of the two inequalities. 相似文献