Existence Theorems for Some Classes of Boundary Value Problems Involving the P(X)-Laplacian
Nonlinear Analysis, 2008 We prove an alternative for a nonlinear eigenvalue problem involving the p(x)-Laplacian and study a subcritical boundary value problem for the same operator.
Ionica Andrei
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Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials
Fractal and Fractional, 2022 This paper deals with a fourth-order elliptic equation with Dirichlet boundary conditions. Using a variant form of the mountain pass theorem, we prove the existence of nontrivial solutions to this problem.
Jiabin Zuo +2 more
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Speculating About Mountains [PDF]
, 1996 ∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology, Bulgaria. ∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science and Technology, Bulgaria.The definition of the weak slope
Krastanov, M. +2 more
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Infinitely Many Solutions for a Class of Fractional Impulsive Coupled Systems with (p,q)-Laplacian
Discrete Dynamics in Nature and Society, 2018 By using the symmetric mountain pass lemma, we investigate the problem of existence of infinitely many solutions for a class of fractional impulsive coupled systems with (p,q)-Laplacian, which possesses mixed type nonlinearities, and the nonlinearities ...
Junping Xie, Xingyong Zhang
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Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds [PDF]
, 1995 ∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.Let M be a complete C1−Finsler manifold without boundary and f : M → R be ...
Krastanov, Mikhail +2 more
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Ground states for superlinear fractional Schr\"odinger equations in \R^{N}
, 2016 In this paper we study ground states of the following fractional Schr\"odinger equation (- \Delta)^{s} u + V(x) u = f(x, u) \, \mbox{ in } \, \R^{N}, u\in \H^{s}(\R^{N}) where $s\in (0,1)$, $N>2s$ and $f$ is a continuous function satisfying a ...
Ambrosio, Vincenzo
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Existence and multiplicity of solutions for divergence type elliptic equations
Electronic Journal of Differential Equations, 2011 We establish the existence and multiplicity of weak solutions of a problem involving a uniformly convex elliptic operator in divergence form. We find one nontrivial solution by the mountain pass lemma, when the nonlinearity has a $(p-1)$-superlinear ...
Lin Zhao, Peihao Zhao, Xiaoxia Xie
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Homoclinic solutions of 2nth-order difference equations containing both advance and retardation
Open Mathematics, 2016 By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation.
Long Yuhua, Zhang Yuanbiao, Shi Haiping
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Existence of multiple solutions for a quasilinear Neumann problem with critical exponent
Boundary Value Problems, 2018 The main purpose of this paper is to establish the existence and multiplicity of nontrivial solutions for a quasilinear Neumann problem with critical exponent.
Yuanxiao Li, Suxia Xia
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Existence of solitons for discrete nonlinear Schrodinger equations
Electronic Journal of Differential Equations, 2016 By using the Mountain Pass Lemma, we establish sufficient conditions for the existence of solitons for the discrete nonlinear Schrodinger equations.
Haiping Shi, Yuanbiao Zhang
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