Results 91 to 100 of about 343 (158)

Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3

Abstract and Applied Analysis, 2014
We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3‍|∇u|2dx)Δu+u=k(x)f(u)+h(x),  x∈R3,  u∈H1(R3),  u>0,  x∈R3, where f is asymptotically linear with respect to t at infinity.
Ling Ding, Lin Li, Jin-Ling Zhang
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Optimality conditions for strongly monotone variational inequalities

, 1993
Necessary conditions for optimal controls have been obtained for strongly monotone variational inequalities by the penalty method, Ekeland's Variational Principle, and lower-semicontinuity of set-valued mappings.
Rubio, J.E., Liu, Wenbin
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Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth

Journal of Function Spaces, 2020
In this paper, we prove the multiplicity of nontrivial solutions for a class of fractional-order elliptic equation with magnetic field. Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the ...
Jianwen Zhou, Bianxiang Zhou, Yanning Wang   +2 more
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Ekeland's inverse function theorem in graded Fréchet spaces revisited for multifunctions

, 2017
Revised versionIn this paper, we present some implicit function theorems for set-valued mappings between Fréchet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle.
Van Ngai Huynh, Huynh, van Ngai, Théra, Michel, Michel Théra   +3 more
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Pontryagin Maximum Principle for Optimal Control of Variational Inequalities

, 1999
International audienceIn this paper we investigate optimal control problems governed by variational inequalities. We present a method for deriving optimality conditions in the form of Pontryagin's principle.
Bergounioux, Maïtine, Zidani, Housnaa
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From Quasi-variational Inclusion Problems to Stampacchia Vector Quasi-equilibrium Problems ,Stampacchia Set-valued Vector Ekeland's Variational Principle and Caristi's Fixed Point Theorem

, 2011
[[abstract]]In this paper, we first study existence theorems of solution for quasivariational inclusion problems. We apply existence theorems of solution for quasivariational inclusion problem to study the existence theorems of solution for the ...
Lai-Jiu Lin; Chih sheng Chuang; Sung- Yu Wang
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Function variational principles and coercivity

, 2005
The function type extension of Ekeland's variational principle [J. Math. Anal. Appl. 47 (1974) 324–353] due to Zhong [Nonlinear Anal. 29 (1997) 1421–1431] is deductible in a simplified manner and in a larger functional context. This is also true for his (
Turinici, Mihai, Mihai Turinici
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On an eigenvalue problem with variable exponents and sign-changing potential

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a sign-changing potential. We prove that any $\lambda>0$ sufficiently small is an eigenvalue of the nonhomogeneous eigenvalue problem \begin{equation ...
Bin Ge
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Existence of solutions for a second order problem on the half-line via Ekeland's variational principle

, 2016
In this paper we study the existence of nontrivial solutions for a nonlinear boundary value problem posed on the half-line.
O’Regan, O’Regan, Bouafia, D., Moussaoui, T.   +2 more
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Pontryagin's principle in the control of semilinear elliptic variational inequalities

, 1989
This paper deals with necessary conditions satisfied by the optimal control of a variational inequality governed by a semilinear operator of elliptic type and a maximal monotone operator b in ÓÊx Ó. A non classical smoothing of b allows us to formulate a
Tiba, D., Bonnans, J. Frederic
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