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Nonlinear Elliptic Eigenvalue Problems
1992As a further application of the direct methods of the calculus of variations let us discuss a special class of nonlinear eigenvalue problems. As far as the technical framework is concerned, we proceed here as in our treatment of nonlinear boundary value problems in Chap.
Philippe Blanchard, Erwin Brüning
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Nonlinear Nonhomogeneous Elliptic Problems
2019We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary).
Nikolaos S. Papageorgiou +2 more
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On a Singular Nonlinear Elliptic Problem
SIAM Journal on Mathematical Analysis, 1986This paper is concerned with the elliptic boundary value problem of the form \[ Lu(x)=-\sum^{n}_{i,j=1}(\partial /\partial x_ i)(a_{ij}(\partial /\partial x_ j)u(x))=f(x,u(x)),\quad for\quad x\in \Omega;\quad u(x)=0\quad for\quad x\in \partial \Omega \] where \(\Omega\) is a bounded region in \(R^ n\), \(n\geq 3\), \(\partial \Omega\) is the boundary ...
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Quasilinear elliptic problems with concave–convex nonlinearities
Communications in Contemporary Mathematics, 2017In this paper, the existence and multiplicity of solutions for a quasilinear elliptic problem driven by the [Formula: see text]-Laplacian operator is established. These solutions are also built as ground state solutions using the Nehari method. The main difficulty arises from the fact that the [Formula: see text]-Laplacian operator is not homogeneous ...
Carvalho, M. L. M. +2 more
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2000
To solve a nonlinear elliptic problem the technique is almost unique: one has to rely on a fixed point argument. To do so one can always first solve the problem at hand on a finite dimensional space — this is where the computer stops its investigations — and in practice this is sufficient. Then, one has to pass to the limit.
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To solve a nonlinear elliptic problem the technique is almost unique: one has to rely on a fixed point argument. To do so one can always first solve the problem at hand on a finite dimensional space — this is where the computer stops its investigations — and in practice this is sufficient. Then, one has to pass to the limit.
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On nonlinear elliptic problems with jumping nonlinearities
Annali di Matematica Pura ed Applicata, 1981Elliptic equations with nonlinearities, which have different derivatives at plus and minus infinity, are studied. A characterization of solvability is given by establishing the existence of nonlinear eigenvalues of a corresponding positive-homogeneous equation.
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Fundamental solutions and nonlinear elliptic critical problems
ANNALI DELL UNIVERSITA DI FERRARA, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jannelli, Enrico, Lazzo, Monica
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Hilbert’s projective metric and nonlinear elliptic problems
Nonlinear Analysis: Theory, Methods & Applications, 2009The paper deals with eigenvalue problems for a class of positive nonlinear operators. Precisely, let \(K\) be a closed (not necessarily solid) cone in a real Banach space \(X,\) and let \(d\) be the Hilbert projective metric in \(K^+=K\setminus\{0\}\). For given \(f\in K^+\) and \(r>0,\) let \(K_f=\{x\in K^+:\;d(x,f)0, \] and the associated fixed point
Huang, Min-Jei +2 more
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Nonlinear elliptic boundary problems
1991We establish estimates and regularity for solutions to nonlinear elliptic boundary problems. In §8.1 we treat completely nonlinear second order equations, obtaining L2-Sobolev estimates for solutions assumed a priori to belong to \({C^{2 + r}}(\overline M )\), r > 0.
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MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH A DISCONTINUOUS NONLINEARITY
Analysis and Applications, 2006We consider a nonlinear elliptic equation driven by the p-Laplacian with a discontinuous nonlinearity. Such problems have a "multivalued" and a "single-valued" interpretation. We are interested in the latter and we prove the existence of at least two distinct solutions, both smooth and one strictly positive.
Filippakis, Michael E. +1 more
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