scholarly journals Multiplicity of solutions for a class of quasilinear problem in exterior domains with Neumann conditions

2004 ◽  
Vol 2004 (3) ◽  
pp. 251-268 ◽  
Author(s):  
Claudianor O. Alves ◽  
Paulo C. Carrião ◽  
Everaldo S. Medeiros
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Exterior Domain ◽  
Neumann Boundary ◽  
Exterior Domains ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problem ◽  
Existence And Multiplicity ◽  
Quasilinear Problem ◽  
Quasilinear Elliptic

We study the existence and multiplicity of solutions for a class of quasilinear elliptic problem in exterior domain with Neumann boundary conditions.

Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds

2015 ◽  
Vol 17 (02) ◽  
pp. 1450029 ◽  
Author(s):  
Silvia Cingolani ◽  
Giuseppina Vannella ◽  
Daniela Visetti
Keyword(s):  
Riemannian Manifold ◽  
Positive Solutions ◽  
Riemannian Manifolds ◽  
Elliptic Problem ◽  
Quasilinear Equations ◽  
Metric Tensor ◽  
Poincaré Polynomial ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Problem ◽  
Quasilinear Elliptic

We consider a compact, connected, orientable, boundaryless Riemannian manifold (M, g) of class C∞ where g denotes the metric tensor. Let n = dim M ≥ 3. Using Morse techniques, we prove the existence of [Formula: see text] nonconstant solutions u ∈ H1,p(M) to the quasilinear problem [Formula: see text] for ε > 0 small enough, where 2 ≤ p < n, p < q < p*, p* = np/(n - p) and [Formula: see text] is the p-laplacian associated to g of u (note that Δ2,g = Δg) and [Formula: see text] denotes the Poincaré polynomial of M. We also establish results of genericity of nondegenerate solutions for the quasilinear elliptic problem (Pε).

scholarly journals Existence and Multiplicity of Nonnegative Solutions for Quasilinear Elliptic Exterior Problems with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Jincheng Huang
Keyword(s):  
Boundary Conditions ◽  
Exterior Domain ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Multiplicity Results ◽  
Exterior Problems ◽  
Existence And Multiplicity ◽  
Nonnegative Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

Existence and multiplicity results are established for quasilinear elliptic problems with nonlinear boundary conditions in an exterior domain. The proofs combine variational methods with a fibering map, due to the competition between the different growths of the nonlinearity and nonlinear boundary term.

scholarly journals Existence and multiplicity of solutions for a p(x)-biharmonic problem with Neumann boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-15
Author(s):  
Fouzia Moradi ◽  
Abdel Rachid El Amrouss ◽  
Mimoun Moussaoui
Keyword(s):  
Boundary Conditions ◽  
Critical Point ◽  
Point Theorem ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Critical Point Theorem ◽  
Multiplicity Of Solutions ◽  
Biharmonic Problem ◽  
Existence And Multiplicity

In this paper, we study the p(x)-biharmonique problem with Neumannboundary conditions. Using the three critical point Theorem, we establish the existence of at least threesolutions of this problem.

scholarly journals Multiplicity of solutions for a nonhomogeneous quasilinear elliptic problem with critical growth

2019 ◽  
Vol 18 (1) ◽  
pp. 83-106
Author(s):  
Marcos L. M. Carvalho ◽  
◽  
José Valdo A. Goncalves ◽  
Claudiney Goulart ◽  
Olímpio H. Miyagaki ◽  
...  
Keyword(s):  
Elliptic Problem ◽  
Critical Growth ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

Quasilinear elliptic problems with concave–convex nonlinearities

2017 ◽  
Vol 19 (06) ◽  
pp. 1650050 ◽  
Author(s):  
M. L. M. Carvalho ◽  
Edcarlos D. da Silva ◽  
C. Goulart
Keyword(s):  
Elliptic Problem ◽  
Ground State ◽  
Nonlinear Term ◽  
Laplacian Operator ◽  
Main Difficulty ◽  
Quasilinear Elliptic Problem ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Problems ◽  
Nehari Method ◽  
Quasilinear Elliptic

In this paper, the existence and multiplicity of solutions for a quasilinear elliptic problem driven by the [Formula: see text]-Laplacian operator is established. These solutions are also built as ground state solutions using the Nehari method. The main difficulty arises from the fact that the [Formula: see text]-Laplacian operator is not homogeneous and the nonlinear term is indefinite.

Three Solutions for a Singular Quasilinear Elliptic Problem

2018 ◽  
Vol 62 (1) ◽  
pp. 179-196 ◽  
Author(s):  
Francesca Faraci ◽  
George Smyrlis
Keyword(s):  
Elliptic Problem ◽  
Weak Solutions ◽  
Singular Term ◽  
High Dimensional ◽  
Three Solutions ◽  
Quasilinear Elliptic Problem ◽  
High Dimensional Case ◽  
Truncation Techniques ◽  
Quasilinear Problem ◽  
Quasilinear Elliptic

AbstractIn the present paper we deal with a quasilinear problem involving a singular term. By combining truncation techniques with variational methods, we prove the existence of three weak solutions. As far as we know, this is the first contribution in this direction in the high-dimensional case.

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