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10 results on '"Amoroso Eleonora"'

1. Two solutions for Dirichlet double phase problems with variable exponents

Author

Amoroso Eleonora, Bonanno Gabriele, D’Aguì Giuseppina, and Winkert Patrick

Subjects
bounded solutions, critical point theory, double phase operator with variable exponents, multiplicity results, superlinear reaction, 35a01, 35b33, 35d30, 35j62, 35j66, Mathematics, QA1-939
Abstract

This paper is devoted to the study of a double phase problem with variable exponents and Dirichlet boundary condition. Based on an abstract critical point theorem, we establish existence results under very general assumptions on the nonlinear term, such as a subcritical growth and a superlinear condition. In particular, we prove the existence of two bounded weak solutions with opposite energy sign and we state some special cases in which they turn out to be nonnegative.

Published
2024
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2. Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition

Author

Amoroso, Eleonora, Crespo-Blanco, Ángel, Pucci, Patrizia, and Winkert, Patrick

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann problems, both of independent interest. Moreover, we study a variable exponent double phase problem with a nonlinear boundary condition and prove the existence of multiple solutions under very general assumptions on the nonlinearities. To be more precise, we get constant sign solutions (nonpositive and nonnegative) via a mountain-pass approach and a sign-changing solution by using an appropriate subset of the corresponding Nehari manifold along with the Brouwer degree and the Quantitative Deformation Lemma.

Published
2023

9. Anisotropic (→p, →q)-Laplacian problems with superlinear nonlinearities.

Author

Amoroso, Eleonora, Sciammetta, Angela, and Winkert, Patrick

Subjects
*NONLINEAR equations
Abstract

In this paper we consider a class of anisotropic (→p, →q)-Laplacian problems with nonlinear right-hand sides that are superlinear at 1. We prove the existence of two nontrivial weak solutions to this kind of problem by applying an abstract critical point theorem under very general assumptions on the data without supposing the Ambrosetti-Rabinowitz condition. [ABSTRACT FROM AUTHOR]

Published
2024
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