Results 21 to 30 of about 869,106 (168)
Modeling angiogenesis under Robin boundary conditions. [PDF]
Quant BiolAbstract In this study, we show an example of a numerical model based on the Keller–Segel system of equations to simulate angiogenesis in response to chemotaxis under Robin boundary conditions, which represent the presence of flux at the tumor. Different parameters of the model are modified to identify key biological factors relevant to the behavior of
Álvarez-Caudevilla P +2 more
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The mountain pass theorem on subsystems of second order arithmetic [PDF]
Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona. Curs: 2023-2024. Tutor: David Fernández-DuqueThe main goal of this work is to formalize the Mountain Pass Theorem of Ambrosetti and Rabinowitz within ...
Aguilar Enríquez, Miguel Alejandro
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Some extensions of the mountain pass lemma
Differential and Integral Equations, 1988 This article deals with some variants of the classical mountain pass lemma. In the first part the following result is obtained: if \(f: \mathbb{E}\to\mathbb{R}\) is a \(C^ 1\) smooth functional with \(PS\)-condition on a real Banach space \(\mathbb{E}\), \(x_ 0,x_ 1\in\mathbb{E}\), \({\mathcal D}\) is an open neighborhood, \(x_ 0,x_ 1\not\in{\mathcal D}
Guo, Da Jun, Sun, Jing Xian, Qi, Gui Jie
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A bounded mountain pass lemma without the (PS) condition and applications [PDF]
Transactions of the American Mathematical Society, 1992 The author's generalization of the fundamental mountain pass lemma is the following: Theorem. Let \(G(u)\in C^ 1(H,R^ 1)\), \(u_ k\) converging weakly to \(u\), \(| G(u_ k)|\leq c\), \(G'(u_ k)\to 0\), imply that \(G'(u)=0\). Assume that \(H=N\oplus M\), \(\dim N0\), such that \[ c_ 0\equiv\max_{bdy\{v\in N\mid\| v\|\leq R_ 0\}}G0 ...
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Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition
Boundary Value Problems, 2009 In this paper, we establish two different existence results of solutions for a nonlocal elliptic equations with nonlinear boundary condition. The first one is based on Galerkin method, and gives a priori estimate. The second one is based on Mountain Pass
Fanglei Wang, Yukun An
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Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds [PDF]
, 1995 Let M be a complete C1−Finsler manifold without boundary and f : M → R be a locally Lipschitz function. The classical proof of the well known deformation lemma can not be extended in this case because integral lines may not exist.
Tsachev, Tsvetomir +2 more
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Some Applications of Generalized Mountain Pass Lemma
, 2014 The Ghoussoub-Preiss's generalized Mountain Pass Lemma with Cerami-Palais-Smale type condition is a generalization of classical MPL of Ambrosetti-Rabinowitz, we apply it to study the existence of the periodic solutions with a given energy for some second order Hamiltonian systems with symmetrical and non-symmetrical potentials.
Li, Fengying, Li, Bingyu, Zhang, Shiqing
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, 1985 Some variants of one of the main results in critical point theory, namely the mountain pass lemma by A. Ambrosetti and P. H. Rabinowitz [J. Funct. Anal. 14 (1973), 349-381], are proved in this paper. In this paper we prove that if X is finite-dimensional,
J. SERRIN, PUCCI, Patrizia
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Existence of solutions to perturbed critical biharmonic equations with Hardy potential
Electronic Journal of Differential EquationsThis article studies a perturbed critical biharmonic equation with Hardy potential. The main challenge arises from the combined effects of critical Sobolev nonlinearity and singular Hardy potential, which induce a double loss of compactness in the ...
Qi Li, Yuzhu Han, Jian Wang
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New Quantitative Deformation Lemma and New Mountain Pass Theorem
, 2014 In this paper, we obtain a new quantitative deformation Lemma so that we can obtain more critical points, especially for supinf critical value $c_1$, $x=φ^{-1}(c_1)$ is a new critical point. For $infmax$ critical value $c_2$, we can obtain two new critical points $x = 0$ (valley point) and $x = e$(peak point) ,comparing with Willem's variant of the ...
Ding, Liang, Zhang, Fode, Zhang, Shiqing
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