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Improved estimates for the Ginzburg-Landau equation : the elliptic case

Fabrice Bethuel, Giandomenico Orlandi, Didier Smets (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the -energy and the parameter . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.

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 ⎧ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, with 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

Francesca Alessio, Paolo Caldiroli, Piero Montecchiari (2001)

Bollettino dell'Unione Matematica Italiana

Si considera una classe di equazioni ellittiche semilineari su della forma con sottocritico (o con nonlinearità più generali) e funzione limitata. In questo articolo viene presentato un risultato di genericità sull'esistenza di infinite soluzioni, rispetto alla classe di coefficienti limitati su e non negativi all'infinito.

Infinitely many solutions for a semilinear elliptic equation in via a perturbation method

Marino Badiale (2002)

Annales Polonici Mathematici

We introduce a method to treat a semilinear elliptic equation in (see equation (1) below). This method is of a perturbative nature. It permits us to skip the problem of lack of compactness of but requires an oscillatory behavior of the potential b.

Infinitely many weak solutions for a non-homogeneous Neumann problem in Orlicz--Sobolev spaces

Ghasem A. Afrouzi, Shaeid Shokooh, Nguyen T. Chung (2019)

Commentationes Mathematicae Universitatis Carolinae

Under a suitable oscillatory behavior either at infinity or at zero of the nonlinear term, the existence of infinitely many weak solutions for a non-homogeneous Neumann problem, in an appropriate Orlicz--Sobolev setting, is proved. The technical approach is based on variational methods.

Integrability for vector-valued minimizers of some variational integrals

Francesco Leonetti, Francesco Siepe (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove that the higher integrability of the data improves on the integrability of minimizers of functionals , whose model is where and .

Interpolation theorem for the p-harmonic transform

Luigi D'Onofrio, Tadeusz Iwaniec (2003)

Studia Mathematica

We establish an interpolation theorem for a class of nonlinear operators in the Lebesgue spaces arising naturally in the study of elliptic PDEs. The prototype of those PDEs is the second order p-harmonic equation . In this example the p-harmonic transform is essentially inverse to . To every vector field our operator assigns the gradient of the solution, . The core of the matter is that we go beyond the natural domain of definition of this operator. Because of nonlinearity our arguments...

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