We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically
...-linear at infinity. The proof relies on a cohomological linking in a product Banach space where the properties of cones of the sublevels are missing, differently from the single quasilinear equation. We also perform critical group computations of the energy functional at the origin, in spite of the lack of its
regularity, to exclude that the found mini-max solution is trivial. Finally, we furnish a local condition which guarantees that the found solution is not semi-trivial.
We consider a Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian (known as a (p,2)-equation) and with a nonlinearity which exhibits asymmetric behavior as s→±∞. More precisely, it ...is (p−1)-superlinear near +∞ (but without satisfying the Ambrosetti–Rabinowitz condition) and it is (p−1)-sublinear near −∞ and possibly resonant with respect to the principal eigenvalue of the p-Laplacian. Using variational tools along with Morse theory we prove a multiplicity theorem generating five nontrivial solutions (one is negative, two are positive, one is nodal and for the fifth we do not have any information about its sign).
In this paper, we study elliptic equations in which the reaction (right hand side) exhibits an asymmetric behavior as
x
→
±
∞
. More precisely, we assume that we have resonance as
x
→
-
∞
, while as
...x
→
+
∞
the equation is superlinear. Using variational tools combined with the theory of critical groups, we prove several multiplicity theorems for nonlinear, nonhomogeneous equations and for semilinear equations (driven by the Laplacian).
In this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at ...infinity to exist. Moreover, we allow the system to be resonant at zero. Under some general conditions, we will establish the existence and multiplicity of nontrivial periodic solutions by using the Morse theory and two critical point theorems.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
On a class of critical Robin problems Leonardi, Salvatore; Papageorgiou, Nikolaos S.
Forum mathematicum,
01/2020, Letnik:
32, Številka:
1
Journal Article
Recenzirano
We consider a nonlinear parametric Robin problem.
In the reaction, there are two terms, one critical and the other locally defined.
Using cut-off techniques, together with variational tools and ...critical groups, we show that, for all small values of the parameter, the problem has at least three nontrivial smooth solutions all with sign information, which converge to zero in
as the parameter
Parametric nonlinear resonant Robin problems Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.
Mathematische Nachrichten,
November 2019, 2019-11-00, 20191101, Letnik:
292, Številka:
11
Journal Article
Recenzirano
Odprti dostop
We consider a nonlinear Robin problem driven by the p‐Laplacian. In the reaction we have the competing effects of two nonlinearities. One term is parametric, strictly (p−1)‐sublinear and the other ...one is (p−1)‐linear and resonant at any nonprincipal variational eigenvalue. Using variational tools from the critical theory (critical groups), we show that for all big values of the parameter λ the problem has at least five nontrivial smooth solutions.
We consider a nonlinear Robin problem driven by a general nonhomogeneous differential operator plus an indefinite potential term. The reaction is of generalized logistic type. Using variational tools ...we prove a multiplicity theorem producing three nontrivial solutions with sign information (positive, negative and nodal). In the particular case of (
p
, 2)-equations, employing also critical groups, we produce a second nodal solution. Our results extend earlier multiplicity results for coercive problems.
We consider an anisotropic
-equation, with a parametric and superlinear reaction term. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, ...four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups.
In this article we show the existence of nontrivial solutions for nonlocal elliptic equations involving the square root of the Laplacian with the nonlinearity failing to have asymptotic limits at ...zero and at infinity. We use a combination of homotopy invariance of critical groups and the topological version of linking theorems.
For more information see https://ejde.math.txstate.edu/special/01/c3/abstr.html
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK