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2. Existence of infinitely many weak solutions for some quasilinear ⃗p(x)-elliptic Neumann problems

Creator:
Ahmed, Ahmed, Ahmedatt, Taghi, Hjiaj, Hassane, and Touzani, Abdelfattah
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Neumann problem, quasilinear elliptic equation, weak solution, variational principle, and anisotropic variable exponent Sobolev space
Language:
English
Description:
We consider the following quasilinear Neumann boundary-value problem of the type − ∑ N i=1 ∂ ⁄ ∂xi ai ( x, ∂u ⁄ ∂xi ) + b(x)|u| p0(x)−2 u = f(x, u) + g(x, u) in Ω, ∂u ⁄ ∂γ = 0 on ∂Ω. We prove the existence of infinitely many weak solutions for our equation in the anisotropic variable exponent Sobolev spaces and we give some examples.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Quasilinear elliptic problems with multivalued terms

Creator:
Halidias, Nikolaos and Papageorgiou, Nikolaos S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
subdifferential, critical point, Palais-Smale condition, Mountain Pass Theorem, Saddle Point Theorem, multivalued term, Dirichlet problem, Neumann problem, p-Laplacian, and Rayleigh quotient
Language:
English
Description:
We study the quasilinear elliptic problem with multivalued terms.We consider the Dirichlet problem with a multivalued term appearing in the equation and a problem of Neumann type with a multivalued term appearing in the boundary condition. Our approach is based on Szulkin’s critical point theory for lower semicontinuous energy functionals.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. The Neumann problem for the Laplace equation on general domains

Creator:
Medková, Dagmar
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Laplace equation, Neumann problem, potential, and boundary integral equation method
Language:
English
Description:
The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set $G$ in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on $\partial G$. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on $G$ a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public