Existence and multiplicity results for double phase problem with nonlinear boundary condition

2021 ◽  
Vol 60 ◽  
pp. 103307
Author(s):  
Na Cui ◽  
Hong-Rui Sun
Keyword(s):  
Boundary Condition ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Phase Problem ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Double Phase ◽  
Double Phase Problem

scholarly journals Singular Finsler Double Phase Problems with Nonlinear Boundary Condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Csaba Farkas ◽  
Alessio Fiscella ◽  
Patrick Winkert
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Variational Methods ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Euclidean Norm ◽  
Phase Problem ◽  
Double Phase ◽  
Truncation Techniques ◽  
Double Phase Problem

Abstract In this paper, we study a singular Finsler double phase problem with a nonlinear boundary condition and perturbations that have a type of critical growth, even on the boundary. Based on variational methods in combination with truncation techniques, we prove the existence of at least one weak solution for this problem under very general assumptions. Even in the case when the Finsler manifold reduces to the Euclidean norm, our work is the first one dealing with a singular double phase problem and nonlinear boundary condition.

scholarly journals Solutions for parametric double phase Robin problems

2021 ◽  
Vol 121 (2) ◽  
pp. 159-170 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Boundary Condition ◽  
Existence Theorems ◽  
Robin Boundary Condition ◽  
Phase Problem ◽  
Double Phase ◽  
Robin Boundary ◽  
Double Phase Problem

We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .

scholarly journals Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jie Yang ◽  
Haibo Chen ◽  
Senli Liu
Keyword(s):  
Mountain Pass Theorem ◽  
Existence Results ◽  
Variable Exponents ◽  
Phase Problem ◽  
Fountain Theorem ◽  
Existence And Multiplicity ◽  
Genus Theory ◽  
Dual Fountain Theorem ◽  
Double Phase ◽  
Double Phase Problem

We consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. Moreover, infinitely many pairs of solutions are provided by applying the Fountain Theorem, Dual Fountain Theorem, and Krasnoselskii’s genus theory.

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