Results 91 to 100 of about 1,002 (168)
Boundary value problems for the 2nd-order Seiberg-Witten equations
Boundary Value Problems, 2005 It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition ℋ is satisfied.
Celso Melchiades Doria
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Quasilinear Problems without the Ambrosetti-Rabinowitz Condition
, 2021 We show the existence of nontrivial solutions for a class of quasilinear problems in which the governing operators depend on the unknown function.
Mugnai, Dimitri +2 more
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Electronic Journal of Differential Equations, 2005 We study the following quasilinear problem with nonlinear boundary conditions $$displaylines{ -Delta_{p}u=lambda a(x)|u|^{p-2}u+k(x)|u|^{q-2}u-h(x)|u|^{s-2}u, quad hbox{in }Omega,cr | abla u|^{p-2} abla ucdoteta+b(x)|u|^{p-2}u=0quad hbox{on ...
Dimitrios A. Kandilakis
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A min-max principle for non-differentiable functions with a weak compactness condition
, 2009 A general critical point result established by Ghoussoub is extended to the case of locally Lipschitz continuous functions satisfying a weak Palais-Smale hypothesis, which includes the so-called non-smooth Cerami condition.
Livrea, Roberto, Marano, Salvatore A.
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Nonlinear elliptic systems with exponential nonlinearities
Electronic Journal of Differential Equations, 2002 In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N)| abla u |^{N-2}u ) = f(x,u,v) quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N)| abla v |^{N-2}v )= g(x,u,v) quad mbox{in } Omega u(x) = v(x) = 0 ...
Said El Manouni, Abdelfattah Touzani
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On the Evolution of Regularized Dirac-Harmonic Maps from Closed Surfaces. [PDF]
Results Math, 2020 Branding V.
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Multiplicity of solutions for a class of elliptic systems in $R^N$
Electronic Journal of Differential Equations, 2006 This article concerns the multiplicity of solutions for the system of equations $$displaylines{ -Delta u + V(epsilon x)u = alpha |u|^{alpha-2}u|v|^{eta}, cr -Delta v + V(epsilon x)v = eta |u|^{alpha}|v|^{eta-2}v }$$ in $mathbb{R}^N$, where $V$ is a ...
Giovany M. Figueiredo
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Infinitely Many Solutions for Schrödinger–Poisson Systems and Schrödinger–Kirchhoff Equations
MathematicsBy applying Clark’s theorem as altered by Liu and Wang and the truncation method, we obtain a sequence of solutions for a Schrödinger–Poisson system −Δu+V(x)u+ϕu=f(u)inR3,−Δϕ=u2inR3 with negative energy.
Shibo Liu
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On the Palais-Smale condition in geometric knot theory
We prove that various families of energies relevant in geometric knot theory satisfy the Palais-Smale condition (PS) on submanifolds of arclength para\-metrized knots. These energies include linear combinations of the Euler-Bernoulli bending energy with a wide variety of non-local knot energies, such as O'Hara's self-repulsive potentials $E^{α,p}
Freches, Nicolas +3 more
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Morse theory by perturbation methods with applications to harmonic maps
, 1981 There are many interesting variational problems for which the Palais-Smale condition cannot be verified. In cases where the Palais-Smale condition can be verified for an approximating integral, and the critical points converge, a Morse theory is valid ...
K. Uhlenbeck
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