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Inertial manifolds for retarded second order in time evolution equations in admissible spaces

Cung The Anh, Le Van Hieu (2013)

Annales Polonici Mathematici

Using the Lyapunov-Perron method, we prove the existence of an inertial manifold for the process associated to a class of non-autonomous semilinear hyperbolic equations with finite delay, where the linear principal part is positive definite with a discrete spectrum having a sufficiently large distance between some two successive spectral points, and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to some admissible function spaces.

Infinite systems of first order PFDEs with mixed conditions

W. Czernous (2008)

Annales Polonici Mathematici

We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems...

Infinitely many positive solutions for the Neumann problem involving the p-Laplacian

Giovanni Anello, Giuseppe Cordaro (2003)

Colloquium Mathematicae

We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ - Δ p u + λ ( x ) | u | p - 2 u = μ f ( x , u ) in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where Ω N is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, λ L ( Ω ) with e s s i n f x Ω λ ( x ) > 0 and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.

Infinitely many solutions for a class of semilinear elliptic equations in R N

Francesca Alessio, Paolo Caldiroli, Piero Montecchiari (2001)

Bollettino dell'Unione Matematica Italiana

Si considera una classe di equazioni ellittiche semilineari su R N della forma - Δ u + u = a x u p - 1 u con p > 1 sottocritico (o con nonlinearità più generali) e a x funzione limitata. In questo articolo viene presentato un risultato di genericità sull'esistenza di infinite soluzioni, rispetto alla classe di coefficienti a x limitati su R N e non negativi all'infinito.

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