19 research outputs found
Existence and regularity results for nonlinear elliptic equations in Orlicz spaces
We are concerned with the existence and regularity of the solutions to the
Dirichlet problem, for a class of quasilinear elliptic equations driven by a
general differential operator, depending on , and with a
convective term . The assumptions on the members of the equation are
formulated in terms of Young's functions, therefore we work in the
Orlicz-Sobolev spaces. After establishing some auxiliary properties, that seem
new in our context, we present two existence and two regularity results. We
conclude with several examples
Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces
Boundary value problems for second-order elliptic equations in divergence
form, whose nonlinearity is governed by a convex function of non-necessarily
power type, are considered. The global boundedness of their solutions is
established under boundary conditions of Dirichlet, or Neumann, or Robin type.
A decisive role in the results is played by optimal forms of Orlicz-Sobolev
embeddings and boundary trace embeddings, which allow for critical growths of
the coefficients.Comment: 34 pages, comments are welcom
Existence of three periodic solutions for a non-autonomous second order system
The purpose of the present paper is to establish a multiplicity result for some differencial system
Infinitely many solutions for a class of differential inclusions involving the p-biharmonic
The existence of inffinitely many solutions for diffierential inclusions depending on two positive parameters and involving the p- biharmonic operator is established via variational methods
Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces
Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established under boundary conditions of Dirichlet, or Neumann, or Robin type. A decisive role in the results is played by optimal forms of Orlicz-Sobolev embeddings and boundary trace embeddings, which allow for critical growths of the coefficients
Bounds for eigenfunctions of the Neumann p-Laplacian on noncompact Riemannian manifolds
Eigenvalue problems for the p-Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L-q- or L-infinity-bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain.Funding Agencies|Italian Ministry of Education, University and Research (MIUR) [2017AYM8XW, 201758MTR2]; GNAMPA of the Italian INdAM -National Institute of High Mathematics</p
Resonant neumann equations with indefinite linear part
We consider aseminonlinear Neumann problem driven by the p- Laplacian plus an indenite and unbounded potential. The reaction of the problem is resonant at with respect to the higher parts of the spectrum. Using critical point theory, truncation and perturbation techniques, Morse theory and the reduction method, we prove two multiplicity theorems. One produces three nontrivial smooth solutions and the second four nontrivial smooth solutions
A nonlinear eigenvalue problem for the periodic scalar p-Laplacian
We study a parametric nonlinear periodic problem driven by the scalar p-Laplacian. We show that if is the first eigenvalue of the periodic scalar p-Laplacian and , then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques