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[16]
**Nikolaos** **S**. **Papageorgiou**

We consider a nonlinear Dirichlet elliptic problem driven by the sum of a p-Laplacian and a Laplacian [a (p, 2)-equation] and with a reaction term, which is superlinear in the positive direction (without satisfying the Ambrosetti–Rabinowitz condition) and sublinear resonant in the negative direction. Resonance can also occur asymptotically at zero. So, we have a double resonance...

We consider a generalized logistic equation driven by the Neumann p-Laplacian and with a reaction that exhibits a superdiffusive kind of behavior. Using variational methods based on the critical point theory, together with truncation and comparison techniques, we show that there exists a critical value \(\lambda _*>0\) of the parameter, such that if \(\lambda >\lambda _*\), the...

concatenate , 0, + and produce
(see Eqs. 3.21, 3.24 and 3.25), so
, such that
So, we can now state the second multiplicity theorem for problem (1.1).
Leszek Gasi nski and **Nikolaos** **S**. **Papageorgiou**
Theorem

Leszek Gasin ski
0
**Nikolaos** **S**. **Papageorgiou**
0
0
N. S. Papageorgiou Department of Mathematics, National Technical University
, Zografou Campus,
15780 Athens, Greece
We consider a nonlinear Neumann

Abstract We consider a nonlinear parametric equation driven by the sum of a p-Laplacian (p > 2 ) and a Laplacian (a (p,2)-equation) with a Carathéodory reaction, which is strictly ( p − 2 ) -sublinear near +∞. Using variational methods coupled with truncation and comparison techniques, we prove a bifurcation-type theorem for the nonlinear eigenvalue problem. So, we show that...

Leszek Gasin ski
0
**Nikolaos** **S**. **Papageorgiou**
0
0
N. S. Papageorgiou Department of Mathematics, National Technical University
, Zografou Campus,
Athens 15780, Greece
We consider a nonlinear elliptic

Leszek Gasin ski
0
**Nikolaos** **S**. **Papageorgiou**
0
0
N. S. Papageorgiou Department of Mathematics, National Technical University
, Zografou Campus,
15780 Athens, Greece
We consider a semilinear Neumann

We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator and with a (p−1)-superlinear Carathéodory reaction. Our formulation incorporates as a special case equations monitored by the p-Laplacian. Using variational methods coupled with truncation techniques and comparison principles, we show that the problem has at least five nontrivial smooth...

Leszek Gasinski
0
**Nikolaos** **S**. **Papageorgiou**
0
pu = div
0
0
Communicated by Rafael D. Benguria. Received: June 25, 2010. Accepted: July 4, 2011
We consider nonlinear elliptic Dirichlet problems with a

Leszek Gasin ski
0
**Nikolaos** **S**. **Papageorgiou**
0
0
N. S. Papageorgiou Department of Mathematics, National Technical University
, Zografou Campus, 15780,
Athens, Greece
We consider a nonlinear

Leszek Gasin ski
0
**Nikolaos** **S**. **Papageorgiou**
0
0
N. S. Papageorgiou Department of Mathematics, National Technical University
, Zografou Campus,
15780 Athens, Greece
We consider nonlinear Neumann

−1 ≥ 0, a contradiction again. Therefore, there
is a critical point y of ϕ such that y ∈/ {0, u0, v0, u, v, y0}. Then y ∈ C1(T )
and solves problem (
1
).
(85)
(86)
(87)
(88)
(89)
**Nikolaos** **S** ... . **Papageorgiou**
Department of Mathematics
National Technical University
Zagrafou Campus
15780 Athens
Greece
e-mail:
[1] Aizicovici , S. , Papageorgiou , N.S. , Staicu , V. : Periodic solutions for second order

Hindawi Publishing Corporation
Fixed Point Theory and Applications
MICHAEL E. FILIPPAKIS AND **NIKOLAOS** **S**. **PAPAGEORGIOU**
0 Michael E. Filippakis: Department of Mathematics, National Technical