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Let Ω be a bounded domain in Rn with n ≥ 3. In this paper we are concerned with the problem of finding u ∈ H01 (Ω) satisfying the nonlinear elliptic problemsΔu + |u|(n+2/n-2) + f(x) = 0 in Ω and u(x) = 0 on ∂Ω, andΔu + u + |u|(n+2/n-2) + f(x) = 0 in Ω and u(x) = 0 on ∂Ω, when of f ∈ L∞(Ω).

Existence of solutions for some nonlinear elliptic equations.

Anane, Aomar, Chakrone, Omar, Chehabi, Mohammed (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions for some quasilinear $\vec{p} (x)$ -elliptic problem with Hardy potential

Elhoussine Azroul, Mohammed Bouziani, Hassane Hjiaj, Ahmed Youssfi (2019)

Mathematica Bohemica

We consider the anisotropic quasilinear elliptic Dirichlet problem $\{\begin{matrix} - \sum_{i = 1}^{N} D^{i} a_{i} (x, u, \nabla u) + {| u |}^{s (x) - 1} u = f + λ \frac{{| u |}^{p_{0} (x) - 2} u}{{| x |}^{p_{0} (x)}} & in Ω, \\ u = 0 & on \partial Ω, \end{matrix}$ where $Ω$ is an open bounded subset of $ℝ^{N}$ containing the origin. We show the existence of entropy solution for this equation where the data $f$ is assumed to be in $L^{1} (Ω)$ and $λ$ is a positive constant.

Existence of solutions for the one-phase and the multi-layer free-boundary problems with the $p$ -Laplacian operator.

Ly, Idrissa, Seck, Diaraf (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions for the $p (x)$ -Laplacian problem with singular term.

Yongqiang, Fu, Mei, Yu (2010)

Boundary Value Problems [electronic only]

Existence of solutions for transversally elliptic left invariant differential operators on nilpotent Lie groups

Linda P. Rothschild (1983)

Journées équations aux dérivées partielles

Existence of solutions of degenerated unilateral problems with $L^{1}$ data

Lahsen Aharouch, Youssef Akdim (2004)

Annales mathématiques Blaise Pascal

In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type $A u + g (x, u, \nabla u) = f - div F,$ where $A$ is a Leray-Lions operator and $g$ is a Carathéodory function having natural growth with respect to $| \nabla u |$ and satisfying the sign condition. The second term is such that, $f \in L^{1} (Ω)$ and $F \in Π_{i = 1}^{N} L^{p^{'}} (Ω, w_{i}^{1 - p^{'}})$ .

Existence of solutions of strongly nonlinear elliptic equations in RN.

Abdelmoujib Benkirane, M. Kbiri Alaoui (2001)

Revista Matemática Complutense

The paper is dedicated to the existence of local solutions of strongly nonlinear equations in RN and the Orlicz spaces framework is used.

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Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.

Existence of solutions for $p (x)$ -Laplacian equations.

Existence of solutions for quasilinear degenerate elliptic equations.

Existence of solutions for quasilinear elliptic boundary value problems in unbounded domains.

Existence of solutions for some elliptic problems with critical Sobolev exponents.

Existence of solutions for some nonlinear elliptic equations.

Existence of solutions for some quasilinear $\vec{p} (x)$ -elliptic problem with Hardy potential

Existence of solutions for the one-phase and the multi-layer free-boundary problems with the $p$ -Laplacian operator.

Existence of solutions for the $p (x)$ -Laplacian problem with singular term.

Existence of solutions for transversally elliptic left invariant differential operators on nilpotent Lie groups

Existence of solutions of degenerated unilateral problems with $L^{1}$ data

Existence of solutions of strongly nonlinear elliptic equations in RN.

Existence of solutions to a superlinear $p$ -Laplacian equation.

Existence of solutions to indefinite quasilinear elliptic problems of $p$ - $q$ -Laplacian type.

Existence of solutions to microhyperbolic boundary value problems

Existence of solutions to $n$ -dimensional pendulum-like equations.

Existence of solutions to nonlocal and singular elliptic problems via Galerkin method.

Existence of solutions to nonlocal and singular variational elliptic inequality via Galerkin method.

Existence of solutions to $p$ -Laplace equations with logarithmic nonlinearity.

Existence of solutions to singular elliptic equations with convection terms via the Galerkin method.

Currently displaying 401 – 420 of 504