Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent
In this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power-like variable reaction term. One of the main features of our work is that the differential operator involves partial derivatives with different variable exponents, so that the functional-analyt...
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| Published in | Journal of mathematical analysis and applications Vol. 340; no. 1; pp. 687 - 698 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
San Diego, CA
Elsevier Inc
01.04.2008
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-247X 1096-0813 |
| DOI | 10.1016/j.jmaa.2007.09.015 |
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| Abstract | In this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power-like variable reaction term. One of the main features of our work is that the differential operator involves partial derivatives with different variable exponents, so that the functional-analytic framework relies upon anisotropic Sobolev and Lebesgue spaces. Existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients. Our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations. |
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| AbstractList | In this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power-like variable reaction term. One of the main features of our work is that the differential operator involves partial derivatives with different variable exponents, so that the functional-analytic framework relies upon anisotropic Sobolev and Lebesgue spaces. Existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients. Our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations. |
| Author | Pucci, Patrizia Rădulescu, Vicenţiu Mihăilescu, Mihai |
| Author_xml | – sequence: 1 givenname: Mihai surname: Mihăilescu fullname: Mihăilescu, Mihai email: mmihailes@yahoo.com organization: Department of Mathematics, University of Craiova, 200585 Craiova, Romania – sequence: 2 givenname: Patrizia surname: Pucci fullname: Pucci, Patrizia email: pucci@dipmat.unipg.it organization: Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy – sequence: 3 givenname: Vicenţiu surname: Rădulescu fullname: Rădulescu, Vicenţiu email: vicentiu.radulescu@math.cnrs.fr organization: Department of Mathematics, University of Craiova, 200585 Craiova, Romania |
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| Snippet | In this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power-like variable reaction term. One of the main... |
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| SubjectTerms | Anisotropic Sobolev spaces Continuous spectrum Exact sciences and technology Functional analysis Mathematical analysis Mathematics Nonhomogeneous differential operators Operator theory Ordinary differential equations Partial differential equations Sciences and techniques of general use Variational methods |
| Title | Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent |
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