Results 231 to 240 of about 511,067 (272)
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, 2014
In this paper, the author considers semilinear elliptic equations of the form $-\Delta u- \frac{\lambda}{|x|^2}u +b(x)\,h(u)=0$ in $\Omega\setminus\{0\}$, where $\lambda$ is a parameter with $-\infty 0$.
F. Cîrstea
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In this paper, the author considers semilinear elliptic equations of the form $-\Delta u- \frac{\lambda}{|x|^2}u +b(x)\,h(u)=0$ in $\Omega\setminus\{0\}$, where $\lambda$ is a parameter with $-\infty 0$.
F. Cîrstea
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Nonlinear Elliptic Equations and Nonassociative Algebras
, 2014This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equation ...
N. Nadirashvili, V. Tkachev, S. Vladut
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1996
Methods of the calculus of variations applied to problems in geometry and classical continuum mechanics often lead to elliptic PDE that are not linear. We discuss a number of examples and some of the developments that have arisen to treat such problems.
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Methods of the calculus of variations applied to problems in geometry and classical continuum mechanics often lead to elliptic PDE that are not linear. We discuss a number of examples and some of the developments that have arisen to treat such problems.
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Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces
Calculus of Variations and Partial Differential Equations, 2018We present the first to date weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables.
Hongjie Dong, N. Krylov
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Nonlinear equations and elliptic curves
Journal of Soviet Mathematics, 1985The main ideas of global “finite-zone integration” are presented, and a detailed analysis is given of applications of the technique developed to some problems based on the theory of elliptic functions. In the work the Peierls model is integrated as an important application of the algebrogeometric spectral theory of difference operators.
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Semilinear elliptic equations with singular nonlinearities
Calculus of Variations and Partial Differential Equations, 2009We prove existence, regularity and nonexistence results for problems whose model is $$-\Delta u = \frac{f(x)}{u^{\gamma}}\quad {{\rm in}\,\Omega},$$ with zero Dirichlet conditions on the boundary of an open, bounded subset Ω of \({\mathbb{R}^{N}}\). Here γ > 0 and f is a nonnegative function on Ω.
BOCCARDO, Lucio, ORSINA, Luigi
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Nonlinear Elliptic Equations with Mixed Singularities
Potential Analysis, 2017We study non-variational degenerate elliptic equations with mixed singular structures, both at the set of critical points and on the ground touching points. No boundary data are imposed and singularities occur along an a priori unknown interior region. We prove that positive solutions have a universal modulus of continuity that does not depend on their
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Global and local behavior of positive solutions of nonlinear elliptic equations
, 1981B. Gidas, J. Spruck
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A nondegeneracy result for a nonlinear elliptic equation
Nonlinear Differential Equations and Applications NoDEA, 2005Let Ω be a smooth bounded domain of \(\mathbb{R}^{N}\) with N ≥ 5. In this paper we prove, for ɛ > 0 small, the nondegeneracy of the solution of the problem $$\left\{ {\begin{array}{*{20}l} { - \Delta u = u^{\frac{{N + 2}} {{N - 2}}} + \varepsilon u} & {{\text{in}}\;\Omega } \\ {u > 0} & {{\text{in}}\;\Omega } \\ {u = 0} & {{\text{on}}\;\partial ...
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Regularity for solutions of nonlinear elliptic equations
1994In this paper we study the Dirichlet problem for two classes of nonlinear elliptic equations. We give regularity results for the solutions when the right hand side and the coefficients of the lower-order terms are in suitable Lorentz spaces, considering also ''limit cases''.
BETTA, MARIA FRANCESCA +2 more
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