The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation i...The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.展开更多
In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …...In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.展开更多
The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mo...The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.展开更多
This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has ...This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.展开更多
The paper studies an evolutionary p(x)-Laplacian equation with a convection term ut=div(ρα|■u|p(x)-2■u)+∑N i=1■bi(u)/■xi,whereρ(x)=dist(x,■Ω),ess inf p(x)=p^->2.To assure the well-posedness of the solutio...The paper studies an evolutionary p(x)-Laplacian equation with a convection term ut=div(ρα|■u|p(x)-2■u)+∑N i=1■bi(u)/■xi,whereρ(x)=dist(x,■Ω),ess inf p(x)=p^->2.To assure the well-posedness of the solutions,the paper shows only a part of the boundary,Σp■■Ω,on which we can impose the boundary value.Σp is determined by the convection term,in particular,when 1<α<(p^--2)/2,Σp={x∈■Ω:bi′(0)ni(x)<0}.So,there is an essential difference between the equation and the usual evolutionary p-Laplacian equation.At last,the existence and the stability of weak solutions are proved under the additional conditionsα<(p^--2)/2 andΣp=■Ω.展开更多
This paper considers a p(x)-Laplacian equation. Under some suitable conditions a strong maximum principle for it is obtained. Our results improve some known ones.
文摘The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.
文摘In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.
基金supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution”, 2017。
文摘The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.
基金Partially supported by the NSF(11271154)of China the 985 program of Jilin University
文摘This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.
基金Supported by the National Natural Science Foundation of China(No.2015J01592,No.2019J01858)
文摘The paper studies an evolutionary p(x)-Laplacian equation with a convection term ut=div(ρα|■u|p(x)-2■u)+∑N i=1■bi(u)/■xi,whereρ(x)=dist(x,■Ω),ess inf p(x)=p^->2.To assure the well-posedness of the solutions,the paper shows only a part of the boundary,Σp■■Ω,on which we can impose the boundary value.Σp is determined by the convection term,in particular,when 1<α<(p^--2)/2,Σp={x∈■Ω:bi′(0)ni(x)<0}.So,there is an essential difference between the equation and the usual evolutionary p-Laplacian equation.At last,the existence and the stability of weak solutions are proved under the additional conditionsα<(p^--2)/2 andΣp=■Ω.
文摘This paper considers a p(x)-Laplacian equation. Under some suitable conditions a strong maximum principle for it is obtained. Our results improve some known ones.
