Results 61 to 70 of about 279 (111)
Existence and multiplicity of nontrivial solutions for double resonance semilinear elliptic problems
Electronic Journal of Differential Equations, 2002 We consider resonance problems at an arbitrary eigenvalue of the Laplacien. We prove the existence of nontrivial solutions for some semilinear elliptic Dirichlet boundary values problems. We also obtain two nontrivial solutions by using Morse theory.
Abdel R. El Amrouss
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Multiplicity of Solutions for Gradient Systems Using Landesman-Lazer Conditions
Abstract and Applied Analysis, 2010 We establish existence and multiplicity of solutions for an elliptic system which presents resonance at infinity of Landesman-Lazer type. In order to describe the resonance, we use an eigenvalue problem with indefinite weights.
Edcarlos D. da Silva
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Multiple solutions of nonlinear fractional elliptic equations via Morse theory
Electronic Journal of Differential Equations, 2017 This article concerns the existence and multiplicity of weak solutions of the nonlinear fractional elliptic problem. We extend some well known results of semilinear Laplacian equations to the nonlocal fractional setting. Using the variational methods
Wei Qi, Lin Zhao, Xingjie Yan
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Morse Theory for Cell Complexes
Advances in Mathematics, 1998 This paper provides a discrete Morse theory for CW-complexes. The author proves an analogue of the main theorems of the classical theory and gets in the context of PL manifolds an interesting formula of the PL Poincaré conjecture. ``The following are equivalent: (1) (PL Poincaré conjecture) Let \(M\) be a PL \(n\)-manifold which is a homotopy \(n ...
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Morse Theory for Continuous Functionals
Journal of Mathematical Analysis and Applications, 1995 In an earlier paper, the author, \textit{M. Degiovanni} and \textit{M. Marzocchi} [Topol. Methods Nonlinear Anal. 1, No. 1, 151-171 (1993; Zbl 0789.58021)] developed some Lyusternik-Schnirelmann theory for (lower semi-) continuous functions \(X \to \mathbb{R} \cup \{\infty\}\) where \(X\) is a complete metric space.
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Multiple solutions to fractional equations without the Ambrosetti-Rabinowitz condition
Electronic Journal of Differential Equations, 2017 In this article we study a class of fractional Laplace equations which do not satisfy the Ambrosetti-Rabinowitz condition (AR-condition). We establish the existence of three nontrivial solutions and of multiple sign changing solutions by using Morse ...
Ruichang Pei, Jihui Zhang, Caochuan Ma
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Existence of solutions to a superlinear p-Laplacian equation
Electronic Journal of Differential Equations, 2001 Using Morse theory, we establish the existence of solutions to the equation $-Delta_p u = f(x,u)$ with Dirichlet boundary conditions. We assume that $int_0^s f(x,t),dt$ lies between the first two eigenvalues of the p-Laplacian.
Shibo Liu
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Cambridge Journal of Mathematics40 pages. v1:This paper is an outgrowth of v1 of arXiv:2211.11712 which has been greatly expanded and separated into 2 papers: (1) the replaced version of arXiv:2211.11712 concerns symplectic manifolds and uses analytic-based method; (2) this paper which defines the general notion of a cone Morse theory for smooth manifolds with respect to any closed ...
Clausen, David +2 more
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Nontrivial solutions for nonlinear elliptic problems via Morse theory
Electronic Journal of Differential Equations, 2006 We prove the existence of nontrivial solutions for perturbations of p-Laplacian. Our approach combine minimax arguments and Morse Theory, under the conditions on the behaviors of the perturbed function $f(x,t)$ or its primitive $F(x,t)$ near infinity and
Abdesslem Ayoujil, Abdel R. El Amrouss
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Morse theory for 𝐺-manifolds [PDF]
Bulletin of the American Mathematical Society, 1965 openaire +2 more sources