Oscillation of linear difference equations in Banach spaces

One can easily show that almost all solutions of the difference equation

     

A nonlinear parabolic equation backward in time: Regularization with new error estimates

Consider a nonlinear backward parabolic problem in the form

     

Spectral theory for perturbed Krein Laplacians in nonsmooth domains

We study spectral properties for HK,Ω, the Krein-von Neumann extension of the perturbed Laplacian −Δ+V defined on , where V is measurable, bounded and nonnegative, in a bounded open set Ω⊂Rn belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class C1,r, r>1/2. In particular, in the aforementioned context we establish the Weyl asymptotic formula

     

Stability of parabolic problems with nonlinear Wentzell boundary conditions

Of concern is the nonlinear uniformly parabolic problem

     

Global bifurcation for equations involving nonhomogeneous operators in an unbounded domain

We study the structure of the set of solutions of a nonlinear equation involving nonhomogeneous operators:

     

On a new class of elliptic systems with nonlinearities of arbitrary growth

We guarantee the existence of infinitely many different pairs of solutions to the system

     

Stability estimates for parabolic problems with Wentzell boundary conditions

Of concern is the uniformly parabolic problem

     

The index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces

This paper is motivated by the problem of computing the index of an isolated critical point for a certain class of nonlinear elliptic operators. Such a class includes operators A which are defined by

     

On an integral operator between Bloch-type spaces on the unit ball

We characterize the boundedness and compactness of the following integral-type operator

     

Nontrivial solutions of some quasilinear problems via a cohomological local splitting

This paper deals with a generalization of the p-Laplacian type boundary value problem

     

On the Cauchy problem for a reaction-diffusion equation with a singular nonlinearity

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

Existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight

We prove the existence of nonnegative solutions to the system

     

Positive solutions of an elliptic equation with negative exponent: Stability and critical power

We study positive solutions of the equation

     

Asymptotic behavior of bounded solutions to a nonhomogeneous second-order evolution equation of monotone type

By using previous results of Djafari Rouhani [B. Djafari Rouhani, Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. Thesis, Yale university, 1981, part I, pp. 1-76; B. Djafari Rouhani, Asymptotic behaviour of quasi-autonomous dissipative systems in Hilbert spaces, J. Math. Anal. Appl. 147 (1990) 465-476; B. Djafari Rouhani, Asymptotic behaviour of almost nonexpansive sequences in a Hilbert space, J. Math. Anal. Appl. 151 (1990) 226-235] for dissipative systems, we study the asymptotic behavior of solutions to the following system of second-order nonhomogeneous evolution equations:

     

Finite Morse index solutions of an elliptic equation with supercritical exponent

We study the behavior of finite Morse index solutions of the equation

     

Positive clustered layered solutions for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of RN:

     

Well-posedness results for triply nonlinear degenerate parabolic equations

We study well-posedness of triply nonlinear degenerate elliptic-parabolic-hyperbolic problems of the kind