Anti-periodic Solutions to Strongly Nonlinear Evolution Equations in Hilbert Spaces
نویسندگان
چکیده
We prove the existence of strong solutions to a nonlinear evolution equation of the form u′(t) + g(t) = f(t) + h(t) g ∈ SL2{∂φ(u(·))} f ∈ SL2{F (·, u(·))} u(0) = −u(T ), in a Hilbert space H, where φ : D(∂φ) ⊂ H → IR+ is a proper, convex, l.s.c. function of compact type, F : [ 0, T ]×D(∂φ)→ 2 is a multifunction which is demiclosed and dominated in some sense by ∂φ and h ∈ L(0, T ;H) is sufficiently small.
منابع مشابه
Stochastic differential inclusions of semimonotone type in Hilbert spaces
In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...
متن کاملPeriodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces
This paper deals with the Periodic boundary value problems for Controlled nonlinear impulsive evolution equations. By using the theory of semigroup and fixed point methods, some conditions ensuring the existence and uniqueness. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.
متن کاملModified F-Expansion Method Applied to Coupled System of Equation
A modified F-expansion method to find the exact traveling wave solutions of two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...
متن کاملStochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered. The coefficients are assumed to have linear growth. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differentia...
متن کاملBackward uniqueness of stochastic parabolic like equations driven by Gaussian multiplicative noise
One proves here the backward uniqueness of solutions to stochastic semilinear parabolic equations and also for the tamed Navier–Stokes equations driven by linearly multiplicative Gaussian noises. Applications to approximate controllability of nonlinear stochastic parabolic equations with initial controllers are given. The method of proof relies on the logarithmic convexity property known to hol...
متن کامل