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In this paper existence and multiplicity of solutions of the elliptic problem $ℒ u + λ_{1} u + μ u^{+} v u^{-} + g (x, u) = f$ in $Ω$ $B u = 0$ on $\partial Ω$ , are discussed provided the parameters $μ$ and $v$ are close to the first eigenvalue $_{1}$ . The sufficient conditions...

Nonlinear elliptic systems with dynamic boundary conditions.

Joachim Escher (1992)

Mathematische Zeitschrift

Nonlinear elliptic systems with exponential nonlinearities.

El Manouni, Said, Touzani, Abdelfattah (2002)

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

Nonlinear equations with natural growth terms and measure data.

Porretta, Alessio (2002)

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

Nonlinear fourth order problems with asymptotically linear nonlinearities

Abir Amor Ben Ali, Makkia Dammak (2024)

Mathematica Bohemica

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

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]

Nonlinear operator equations and boundary-value problems

Walter Petry (1974)

Commentationes Mathematicae Universitatis Carolinae

Nonlinear perturbation of balayage spaces.

Baalal, Azeddine, Hansen, Wolfard (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

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

Peter Hess (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Nonlinear potential equations with linear parts at resonance

Svatopluk Fučík (1978)

Časopis pro pěstování matematiky

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

Heinrich Begehr, Gerald N. Hile (1982)

Mathematische Zeitschrift

Nonlinear subelliptic Schrödinger equations with external magnetic field.

Tintarev, Kyril (2004)

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

Nonlinear unilateral problems in Orlicz spaces

L. Aharouch, E. Azroul, M. Rhoudaf (2006)

Applicationes Mathematicae

We prove the existence of solutions of the unilateral problem for equations of the type Au - divϕ(u) = μ in Orlicz spaces, where A is a Leray-Lions operator defined on $(A) \subset W ₀ ¹ L_{M} (Ω)$ , $μ \in L ¹ (Ω) + W^{- 1} E_{M ̅} (Ω)$ and $ϕ \in C ⁰ (ℝ, ℝ^{N})$ .

Nonlocal elliptic problems

Andrzej Krzywicki, Tadeusz Nadzieja (2000)

Banach Center Publications

Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem $- Δ φ = M f (φ) / ({(\int_{Ω} f (φ))}^{p})$ , ${φ |}_{Ω} = 0$ are given.

Non-local Gel'fand problem in higher dimensions

Tosiya Miyasita, Takashi Suzuki (2004)

Banach Center Publications

The non-local Gel’fand problem, $Δ v + λ e^{v} / \int_{Ω} e^{v} d x = 0$ with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.

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