Morse Indices at Mountain Pass Orbits of Symmetric Functionals

2002 ◽  
pp. 1-13
Author(s):  
M. Clapp
Keyword(s):  
Mountain Pass ◽  
Morse Indices

NON-RADIALLY SYMMETRIC SOLUTIONS FOR A SUPERLINEAR AMBROSETTI–PRODI TYPE PROBLEM IN A BALL

2005 ◽  
Vol 07 (06) ◽  
pp. 849-866 ◽  
Author(s):  
DJAIRO G. DE FIGUEIREDO ◽  
P. N. SRIKANTH ◽  
SANJIBAN SANTRA
Keyword(s):  
Symmetric Functions ◽  
Mountain Pass Theorem ◽  
Careful Analysis ◽  
Mountain Pass ◽  
Type Problem ◽  
Radially Symmetric Solutions ◽  
Lagrange Functional ◽  
Morse Indices

Using a careful analysis of the Morse indices of the solutions obtained by using the Mountain Pass Theorem applied to the associated Euler–Lagrange functional acting both in the full space [Formula: see text] and in its subspace of radially symmetric functions, we prove the existence of non-radially symmetric solutions of a problem of Ambrosetti–Prodi type in a ball.

scholarly journals Existence and multiplicity of solutions for class of Navier boundary $p$-biharmonic problem near resonance

2014 ◽  
Vol 32 (2) ◽  
pp. 83 ◽  
Author(s):  
Mohammed Massar ◽  
EL Miloud Hssini ◽  
Najib Tsouli
Keyword(s):  
Saddle Point ◽  
Point Theorem ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Saddle Point Theorem ◽  
Biharmonic Problem ◽  
Existence And Multiplicity ◽  
Near Resonance

This paper studies the existence and multiplicity of weak solutions for the following elliptic problem\\$\Delta(\rho|\Delta u|^{p-2}\Delta u)=\lambda m(x)|u|^{p-2}u+f(x,u)+h(x)$ in $\Omega,$\\$u=\Delta u=0$ on $\partial\Omega.$By using Ekeland's variationalprinciple, Mountain pass theorem and saddle point theorem, theexistence and multiplicity of weak solutions are established.

Chemical‐petrographic and isotopic characterization of the volcanic pavement along the ancient Appia route at the Aurunci Mountain Pass, Italy: Insights on possible provenance

2019 ◽  
Vol 34 (5) ◽  
pp. 522-539
Author(s):  
Emiliano Di Luzio ◽  
Ilenia Arienzo ◽  
Simona Boccuti ◽  
Anna De Meo ◽  
Gianluca Sottili
Keyword(s):  
Mountain Pass ◽  
Isotopic Characterization

Fractional elliptic equations with critical exponential nonlinearity

2016 ◽  
Vol 5 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Jacques Giacomoni ◽  
Pawan Kumar Mishra ◽  
K. Sreenadh
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Fractional Laplacian ◽  
Nehari Manifold ◽  
Mountain Pass ◽  
Laplacian Operator ◽  
Exponential Nonlinearity ◽  
Existence Of Positive Solutions ◽  
Fractional Laplacian Operator

AbstractWe study the existence of positive solutions for fractional elliptic equations of the type (-Δ)1/2u = h(u), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1) where h is a real valued function that behaves like eu2 as u → ∞ . Here (-Δ)1/2 is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near t = 0. In case h is concave near t = 0, we show the existence of multiple solutions for suitable range of λ by analyzing the fibering maps and the corresponding Nehari manifold.

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