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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)
Giuseppe Failla +2 more
exaly +2 more sources
Nonlinear Analysis: Theory, Methods & Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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
openaire +4 more sources
A multiplicity theorem for parametric superlinear (p,q)-equations [PDF]
Opuscula Mathematica, 2020 We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition.
Florin-Iulian Onete +2 more
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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 +3 more sources
Nodal and constant sign solutions for singular elliptic problems
, 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
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Nonlinear nonhomogeneous Neumann eigenvalue problems
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
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Resonant Anisotropic (p,q)-Equations
Mathematics, 2020 We consider an anisotropic Dirichlet problem which is driven by the (p(z),q(z))-Laplacian (that is, the sum of a p(z)-Laplacian and a q(z)-Laplacian), The reaction (source) term, is a Carathéodory function which asymptotically as x±∞ can be resonant with
Leszek Gasiński +1 more
doaj +1 more source
Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities [PDF]
Methods and Applications of Analysis, 2015 We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and ”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation and comparison techniques, we show that for all small values of the parameter
Aizicovici, S. +2 more
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OPTIMUM DESIGN OF A STATICALLY DEFINABLE BEAM WITH LIMITATION ON THE MAXIMUM BEAM DEFLECTION
Авіаційно-космічна техніка та технологія, 2020 Here is solved the optimization problem for the longitudinal depth distribution in the beam with a limitation on the maximum value of deflection. A review of the references is done, and it is shown that the known solutions are either erroneous, because ...
Сергей Сергеевич Куреннов
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