Results 11 to 20 of about 1,540 (202)
Constant Sign and Nodal Solutions for Variable Exponent Double Phase Problem
Results in MathematicsLet \(\Omega \subseteq \mathbb{R}^N\) (\(N \geq 2\)) be a bounded domain with Lipschitz boundary \(\partial \Omega\). The authors study the following nonlinear problem \[ - \Delta^a_p u - \Delta_q u = f(z,u) \mbox{ in }\Omega, \quad u\big|_{\partial \Omega}=0, \] in the case of variable exponents \(p,q \in C(\overline{\Omega})\) with \(1< q(x)
Leszek Gasiński +1 more
exaly +3 more sources
Constant sign and nodal solutions for parametric anisotropic (p, 2) -equations [PDF]
Applicable Analysis, 2021 We consider an anisotropic $(p,2)$-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).
Nikolaos S. Papageorgiou +2 more
core +8 more sources
Constant sign and nodal solutions for anisotropic eigenvalue problems
PositivityAbstract We consider a nonlinear eigenvalue problem driven by the anisotropic (p, q)-Laplacian. Using variational tools, truncations, comparisons and critical groups, we show that for all small values of the parameter, the problem has extremal constant sign solutions and nodal solutions. These solutions are ordered and vanish in
Eylem Öztürk, Nikolaos S Papageorgiou
exaly +5 more sources
Nodal and constant sign solutions for singular elliptic problems [PDF]
, 2023 We establish the existence of multiple solutions for singular quasilinear elliptic problems with a precise sign information: two opposite constant sign solutions and a nodal solution. The approach combines sub-supersolutions method and Leray-Schauder topological degree involving perturbation argument.
Motreanu, Dumitru, Moussaoui, Abdelkrim
core +4 more sources
Constant sign and nodal solutions for resonant double phase problems
Annales Fennici Mathematici, 2023 We consider a double phase Dirichlet problem with a reaction which asymptotically as \(x \rightarrow \pm \infty\) can be resonant with respect to the principle eigenvalue \(\hat{\lambda}_{1}>0\) of the Dirichlet weighted \(p\)-Laplacian. Using variational tools, together with truncation and comparison techniques and critical groups, we show that the
Papageorgiou, Nikolaos S. +2 more
openaire +4 more sources
, 2023 We establish the existence of three solutions for singular semilinear elliptic system, two of which are of opposite constant-sign. Under a strong singularity effect, the third solution is nodal with synchronous sign components. The approach combines sub-supersolutions method and Leray-Schauder topological degree involving perturbation argument.
Moussaoui, Abdelkrim
core +4 more sources
Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters
International Journal of Differential Equations, 2010 The study of multiple solutions for quasilinear elliptic problems under Dirichlet or nonlinear Neumann type boundary conditions has received much attention over the last decades.
Siegfried Carl, Dumitru Motreanu
doaj +2 more sources
Nonlinear nonhomogeneous Neumann eigenvalue problems [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2015 We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero.
Pasquale Candito +2 more
doaj +3 more sources
Existence and Multiplicity of Solutions for Resonant (p,2)-Equations
Advanced Nonlinear Studies, 2018 We consider Dirichlet elliptic equations driven by the sum of a p-Laplacian ...
Papageorgiou Nikolaos S. +2 more
doaj +2 more sources
Positive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems [PDF]
Electronic Journal of Differential Equations, 2020 We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition.
Nikolaos S. Papageorgiou +2 more
doaj +2 more sources