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We investigate some nonlinear elliptic problems of the form $Δ^{2} v + σ (x) v = h (x, v) in Ω, v = Δ v = 0 on \partial Ω, (P)$ where $Ω$ is a regular bounded domain in $ℝ^{N}$ , $N \geq 2$ , $σ (x)$ a positive function in $L^{\infty} (Ω)$ , and the nonlinearity $h (x, t)$ is indefinite. We prove the existence of solutions to the problem (P) when the function $h (x, t)$ is asymptotically linear at infinity by using variational method but without the Ambrosetti-Rabinowitz condition. Also, we consider the case when the nonlinearities are superlinear and subcritical.

Nonlinear functional integrodifferential equations in Hilbert space.

Park, J.Y., Lee, S.Y., Lee, M.J. (1999)

International Journal of Mathematics and Mathematical Sciences

Nonlinear homogeneous eigenvalue problem in $R^{N}$ : nonstandard variational approach

Pavel Drábek, Zakaria Moudan, Abdelfettah Touzani (1997)

Commentationes Mathematicae Universitatis Carolinae

The nonlinear eigenvalue problem for p-Laplacian $\{\begin{matrix} - {div (a (x) | \nabla u |}^{p - 2} {\nabla u) = λ g (x) | u |}^{p - 2} u in ℝ^{N}, u > 0 in ℝ^{N}, lim_{| x | \to \infty} u (x) = 0, \end{matrix}$ is considered. We assume that $1 < p < N$ and that $g$ is indefinite weight function. The existence and $C^{1, α}$ -regularity of the weak solution is proved.

Non-linear initial data for second and higher order semi-linear elliptic equations.

James Conlan, Robert P. Gilbert (1975)

Journal für die reine und angewandte Mathematik

Nonlinear Neumann problems on bounded Lipschitz domains.

Siai, Abdelmajid (2005)

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

Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion

Jean-François Delmas, Pascal Vogt (2005)

Annales de l'I.H.P. Probabilités et statistiques

Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B_{p, q}^{s}$ and $F_{p, q}^{s}$

Jens Franke, Thomas Runst (1988)

Czechoslovak Mathematical Journal

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Nonlinear elliptic systems in stochastic game theory.

Nonlinear elliptic systems with dynamic boundary conditions.

Nonlinear elliptic systems with exponential nonlinearities.

Nonlinear Elliptic Systems with Quadratic Growth.

Nonlinear equations with natural growth terms and measure data.

Nonlinear fourth order problems with asymptotically linear nonlinearities

Nonlinear functional integrodifferential equations in Hilbert space.

Nonlinear homogeneous eigenvalue problem in $R^{N}$ : nonstandard variational approach

Non-linear initial data for second and higher order semi-linear elliptic equations.

Nonlinear Neumann problems on bounded Lipschitz domains.

Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion

Nonlinear oblique boundary value problems for hessian equations in two dimensions

Nonlinear operator equations and boundary-value problems

Nonlinear perturbation of balayage spaces.

Nonlinear perturbations of linear elliptic and parabolic problems at resonance : existence of multiple solutions

Nonlinear perturbations of linear non-invertible boundary value problems in function spaces of type $B_{p, q}^{s}$ and $F_{p, q}^{s}$

Nonlinear potential equations with linear parts at resonance

Nonlinear problems with solutions exhibiting a free boundary on the boundary

Nonlinear Riemann Boundary Value Problems for a Nonlinear Elliptic System in the Plane.

Nonlinear subelliptic Schrödinger equations with external magnetic field.

Currently displaying 2601 – 2620 of 5493