Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian
Copyright policy )Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian
AbstractWe are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic-Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to Bonanno and Marano, we guarantee the existence of at least three weak solutions for the problem in a special case.
- University of Messina Italy
- National Institute for Nuclear Physics Italy
- Missouri University of Science and Technology United States
- Razi University Iran (Islamic Republic of)
Statistics and Probability, variational methods, Neumann problem, Variational methods applied to PDEs, Boundary value problems for second-order elliptic equations, 35k57, QA1-939, -laplacian operator, Quasilinear elliptic equations with \(p\)-Laplacian, variational principle, Numerical Analysis, p(x)-Laplacian operator, Neumann elliptic problem, weak solution, variational principle, anisotropic variable exponent Sobolev space., anisotropic variable exponent sobolev space, Applied Mathematics, 37a30, weak solution, Existence problems for PDEs: global existence, local existence, non-existence, 34c27, \(\vec{p}(x)\)-Laplacian, 35b15, 34k14, existence of solutions, neumann elliptic problem, Analysis, Mathematics
Statistics and Probability, variational methods, Neumann problem, Variational methods applied to PDEs, Boundary value problems for second-order elliptic equations, 35k57, QA1-939, -laplacian operator, Quasilinear elliptic equations with \(p\)-Laplacian, variational principle, Numerical Analysis, p(x)-Laplacian operator, Neumann elliptic problem, weak solution, variational principle, anisotropic variable exponent Sobolev space., anisotropic variable exponent sobolev space, Applied Mathematics, 37a30, weak solution, Existence problems for PDEs: global existence, local existence, non-existence, 34c27, \(\vec{p}(x)\)-Laplacian, 35b15, 34k14, existence of solutions, neumann elliptic problem, Analysis, Mathematics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!