Results 121 to 130 of about 1,211,113 (146)

Fucik Spectrum, Sign-Changing, and Multiple Solutions for Semilinear Elliptic Boundary Value Problems with Resonance at Infinity [PDF]

Journal of Mathematical Analysis and Applications, 2000
The Fučik spectrum and the theory of ordinary differential operators in Banach spaces are used to study semilinear elliptic boundary-value problems with jumping nonlinearities with zero or infinities, especially resonances of infinity. Results for the existence of multiple solutions and sign-changing solutions are obtained.
E N Dancer
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Fucik spectrum for operators with rapidly increasing weight and applications

Electronic Journal of Differential Equations
In this article, we study the Fucik spectrum for operators with rapidly increasing weight, which is defined as a set \(\Sigma\) comprising those  \((\alpha, \beta) \in \mathbb{R}^2\) such that$$\displaylines{L u:=-\Delta u-\frac{1}{2}(x \cdot \nabla u)=\alpha u^{+}-\beta u^{-}, \quad\text{in } \mathbb{R}^N,\cru\in X,}$$ has a non-trivial solution \(u\),
Jinzi Bai, Fei Fang
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Double resonance problems with respect to the Fucik spectrum

Indiana University Mathematics Journal, 2003
The authors prove the existence of nontrivial solutions for semilinear elliptic boundary value problems with jumping nonlinearities that have resonance with respect to the Fučík spectrum of the asymptotic part both at zero and at infinity.
Kanishka Perera
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Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity

Science in China Series A: Mathematics, 2001
This paper is devoted to study semilinear elliptic boundary value problem, that is; \[ -\Delta u=f(u)\quad\text{in }\Omega, \qquad u|_{\partial\Omega}=0, \tag{1} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb R^n\). The authors compute that critical groups of zero and infinity to get a nontrivial solution.
Zhitao Zhang
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The Fučík spectrum of the discrete Dirichlet operator

Linear Algebra and its Applications, 2018
The authors deal with a discrete Dirichlet operator of second kind, investigate its Fucik spectrum and describe all Fucik curves. They discuss the properties of the solutions of the linear initial value problem, investigate continuous extension of a solution of semilinear initial value problem, localize all generalized zeros and obtain several ...
Iveta Looseová, Petr Nečesal
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On the First Curve in the Fučik Spectrum of a Mixed Problem

2020
info:eu-repo/semantics ...
Gossez, Jean-Pierre, Marcos, A.
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Type (II) regions between curves of the Fucik spectrum

Nonlinear Differential Equations and Applications, 1997
The Fucik spectrum arises in the study of semilinear elliptic boundary value problems of the form (1) \(Au=f(x,u)\), where \(A\) is a selfadjoint operator having compact resolvent on \(L^2(\Omega)\), \(\Omega\subset \mathbb{R}^n\), and \(f(x,t)\) is a Carathéodory function on \(\overline\Omega \times\mathbb{R}\) such that \(f(x,t)/t\to a\) a.e.
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Some remarks about the Fucik spectrum and application to equations with jumping nonlinearities

Differential and Integral Equations, 2002
The author studies the Fučík spectrum for a selfadjoint operator \(L: D(L)\subset L^2(\Omega)\rightarrow L^2(\Omega)\) near a multiple eigenvalue of \(L\). For further results see \textit{A. K. Ben-Naoum, C. Fabry} and \textit{D. Smets} [Proc. R. Soc. Edinb., Sect. A, Math. 131, 241-265 (2001; Zbl 0987.35118)].
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A variational approach to nonresonance with respect to the Fučik spectrum

Nonlinear Analysis: Theory, Methods & Applications, 1992
The paper is concerned with the periodic problem (1) \(-u''(t) = f(t,u(t))\) in \([0,2\pi]\), \(u(0) = u(2 \pi)\), \(u'(0) = u'(2\pi)\). The authors give sufficient conditions for the existence of at least one solution \(u\) of (1) in \(H^ 2(0,2\pi)\). The nonlinearity \(f(t,s)\) interferes in a certain sense with the associated Fučík spectrum.
Gossez, Jean-Pierre, Cuesta, M.
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The Fučík Spectrum

1999
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