The structure of the critical set in the mountain pass theorem [PDF]
Transactions of the American Mathematical Society, 1987 We show that the critical set generated by the Mountain Pass Theorem of Ambrosetti and Rabinowitz must have a well-defined structure. In particular, if the underlying Banach space is infinite dimensional then either the critical set contains a saddle point of mountain-pass type, or the set of local minima intersects at least
PUCCI, Patrizia, J. SERRIN
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A Mountain Pass-type Theorem for Vector-valued Functions [PDF]
Set-Valued and Variational Analysis, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bednarczuk, E +2 more
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Image restoration via Picard's and Mountain-pass Theorems
Electronic Research Archive, 2022 <abstract><p>In this work, we present existence results for some problems which arise in image processing namely image restoration. Our essential tools are Picard's fixed point theorem for a strict contraction and Mountain-pass Theorem for critical point.</p></abstract>
Souad Ayadi, Özgür Ege
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Existence and multiplicity of positive solutions for a singular system via sub-supersolution method and Mountain Pass Theorem [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper we show existence and multiplicity of positive solutions using the sub-supersolution method and Mountain Pass Theorem in a general singular system which the operator is not homogeneous neither linear.
Suellen Arruda, Rubia Nascimento
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Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Damped Vibration Problems with Impulsive Effects [PDF]
Abstract and Applied Analysis, 2014 This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects.
Qiongfen Zhang
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Multiplicity of positive solutions for second order quasilinear equations [PDF]
Mathematica Bohemica, 2020 We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
Dahmane Bouafia +2 more
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Periodic solutions for second-order Hamiltonian systems with the p-Laplacian
Electronic Journal of Differential Equations, 2006 In this paper, we investigate the periodic solutions of Hamiltonian system with the p-Laplacian. By using Mountain Pass Theorem the existence of at least one periodic solution is obtained, Furthermore, under suitable assumptions, we obtain the ...
Weigao Ge, Yu Tian
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The mountain pass theorem on subsystems of second order arithmetic [PDF]
The main goal of this work is to formalize the Mountain Pass Theorem of Ambrosetti and Rabinowitz within the formal subsystem of second order arithmetic known as ACA0. We develop some Analysis within this system to have access to the space of continuous functions from [0, 1] into a separable Banach space and from there built formalized proofs of the ...
Aguilar Enríquez, Miguel Alejandro
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GENERAL QUASILINEAR PROBLEMS INVOLVING \(p(x)\)-LAPLACIAN WITH ROBIN BOUNDARY CONDITION
Ural Mathematical Journal, 2020 This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving \(p(x)\)-Laplace type equation, namely $$ \left\{\begin{array}{lll} -\mathrm{div}\, (a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u ...
Hassan Belaouidel +2 more
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Nontrivial Solutions for Asymmetric Kirchhoff Type Problems
Abstract and Applied Analysis, 2014 We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞ in ℝN(N=2,3). Namely, it is 4-linear at −∞ and 4-superlinear at +∞.
Ruichang Pei, Jihui Zhang
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