Displaying similar documents to “Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket”

Non-trivial solutions for a two-point boundary value problem

G. A. Afrouzi, A. Hadjian, S. Heidarkhani (2013)

Annales Polonici Mathematici

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We prove the existence of at least one non-trivial solution for Dirichlet quasilinear elliptic problems. The approach is based on variational methods.

New variational principle and duality for an abstract semilinear Dirichlet problem

Marek Galewski (2003)

Annales Polonici Mathematici

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A new variational principle and duality for the problem Lu = ∇G(u) are provided, where L is a positive definite and selfadjoint operator and ∇G is a continuous gradient mapping such that G satisfies superquadratic growth conditions. The results obtained may be applied to Dirichlet problems for both ordinary and partial differential equations.

On the existence of multiple positive solutions for a certain class of elliptic problems

Aleksandra Orpel (2004)

Banach Center Publications

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We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.

On a comparison principle for a quasilinear elliptic boundary value problem of a nonmonotone type

Michal Křížek, Liping Liu (1996)

Applicationes Mathematicae

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A nonlinear elliptic partial differential equation with the Newton boundary conditions is examined. We prove that for greater data we get a greater weak solution. This is the so-called comparison principle. It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.

Existence for a Cauchy-Dirichlet problem for evolutional p-Laplacian systems

Masashi Misawa (2004)

Applicationes Mathematicae

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We study the existence of a weak solution to a Cauchy-Dirichlet problem for evolutional p-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional p-Laplacian system with an L¹-function as external force. The key ingredient is the maximum principle for weak solutions.

Weak compactness of solutions for fourth order elliptic systems with critical growth

Paweł Goldstein, Paweł Strzelecki, Anna Zatorska-Goldstein (2013)

Studia Mathematica

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We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.

A Dirichlet problem with asymptotically linear and changing sign nonlinearity.

Marcello Lucia, Paola Magrone, Huan-Song Zhou (2003)

Revista Matemática Complutense

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This paper deals with the problem of finding positive solutions to the equation -∆[u] = g(x,u) on a bounded domain 'Omega' with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour. The solutions are found using the Mountain Pass Theorem.